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I spend most of my free time now a days reading about PIs and their Pubmed pages, trying to figure out where to go for rotations. Since I'm interested in translational research more, I found most of the PIs publish their work in journals with impact factors range from 3 - 10. Ones publish in Nature and Science are usually basic research, at least at this school. As you may know from my previous post, I'm not quite happy with the school ( and the only option ) I'm going to this full. I thought I'd compensate this low achievement by working harder in grad school and publish in top journal. 
Another thing, which might sound horrible stereotype, I was advised by two friends, one of them is a postdoc. other is a grad student to avoid PIs from China and India. Their reasoning that PIs from those two countries are usually demanding and expect their students to stay for longer time in grad school than average. But again I'm aiming to publish at top journals, which might require staying for longer time. 
What do you think? 

Indiana was the only interview I got. I've been trying to avoid grad school for the past two years, applied to a lot of postdoc. positions, impossible to get without being a first author. I decided to go to Indiana. Thank you for your input everyone. 

A few things, not all of them are the nicest comments:
1) Research is probably one of the fields that requires the most self-motivation. If you're not passionate about your current work and it shows (which it sounds like it does with you - especially if it's to the point where your mentors comment on it), that's going to be a difficult hurdle moving forward. If you don't like the projects that you're working on, "lemons into lemonade" seems to be the best cliché phrase that can be used here.
2) If you want to reapply and apply places that are leading the field of cancer immunotherapy - whether it's Sloan Kettering, UPenn, UW/FHCRC, or Harvard/DFCI - you're going to need three letter that are excellent. If you have any doubts about your letter writers you need to find new ones. A letter saying that you did well probably is not going to get you an interview at programs that are leaders in the field. Stop worrying about credentials. If the individual is someone that can attest to your research experience, then a strong letter from them would almost certainly be better than a generic or weak letter from a department chair somewhere else (and if they can't attest to your research experience, that's a different issue).
3) The GRE thing is something you recognize. Part of me wonders if for higher level programs international students need higher GRE scores - I can't really comment on this.
4) This goes back to the self-motivation thing - are you willing to do a lot of work over the next nine months to get to a place where you are competitive? Do you know how to make the most out of your next year? I'm not certain where else you interviewed, but if you have good stats and the functional equivalent of a doctorate already, I just don't see your GRE score being the complete dealbreaker here (I'm also quite firmly of the belief that statistics aren't the end all, be all of the process - unlike our resident biostatistician). Moreover, if you did interview other places, maybe asking what went wrong there is something you should do sooner rather than later.

Okay.  I can see where you'd want to reapply.  And you might get in somewhere better, I can't really say.  But.  I think you issue would be your letter of recommendations.  One bad letter of recommendation, or even a mediocre one, can shoot down an application.  It says a few things that I think @immuno91 mentioned; it can emphasize a lack of self-motivation.  Also, it can say that maybe you aren't the best at self-evaluation (if in your SoP if you talked yourself up but your LW was a little more like, "eh, they were okay,")  or that you aren't actually capable of performing in a research environment.  It matters what the adcoms think of you from the faculty who write to them about you.  It doesn't matter if your experiences were at top schools are not.
So I think your GRE is probably a secondary issue.  I am sorry your cycle didn't turn out the way you wanted it to.  I would find some new letter writers.  Maybe you a post bacc or get a job related to your field of choice or go to a master's program.  If you don't want to do that, and you reapply next fall with the same profile, you run the risk of similar results next fall.

What about doing a post bacc or a master's?  The bottom line is that you can't change your profile enough in the nine months before submission.  The GRE is easy to fix, recommendations are not.  And again, I'm going to reiterate... Don't worry about their credentials.  Everybody cares more about what they say about you anyway.  And if you think they are saying anything less than glowing, you need to not use them again.
You can be successful at a lower ranked school.  However, going to somewhere premier really greases the wheels in terms of networking and exposure. Unfortunately, the quality and number of international students at such schools is high and low, respectively, because of competition.  I think you need to reevaluate how to change your profile in terms of GRE and letters as well as if it would be worth it to reapply with only the top programs in the US in mind.

What makes you want to do cancer immunotherapy? I did my undergrad thesis in cancer immunology, and I would say there are really only a handful of people at a handful of places doing purely translational work. Let's put it this way: do you want to do your PhD working on a topic like optimizing CAR T cells so they are 10% cheaper for the clinic, or do you want to do your PhD working on a topic like understanding why certain cancers elicit an immune response and why others don't. Don't get me wrong-- I agree that the field is hot, but because it's quite interdisciplinary, for young researchers it can be quite challenging. I'm one of those people who think that the purpose of graduate school is to not necessarily find the next Nobel prize-winning discovery, but to learn how to do good science.  
It's unfortunate that your letters are not great (if they are what you believe them to be). You're right in that you can't change them, but you should also realize that they are the number one or number two most important part of your graduate school application. If you can take a year off to work in the lab and have your current PI write a glowing letter (specifically addressing how you have found your motivation and are a changed person), then it would be worthwhile to retake the GRE and reapply next cycle. Otherwise, I think IU is a good school to pursue your PHD-- there are great, reputable PI's there, and while there may not be a cancer immunotherapy center like one you see at Sloan Kettering or MD Anderson, you will find a lab that will teach you the fundamentals on how to think like any cancer immunologist. If you read up a bit on the history, you'll realize that most of the "giants" were trained as fundamental immunologists or molecular biologists and slowly migrated into the field after they had already established their own labs.
tl;dr You don't need to train as a cancer immunologist to become a great cancer immunologist, and the work you do as a PhD student may not represent your greatest contribution to science

Even if you start contacting them now, I wouldn't set up more than the first rotation. You won't know who you'll want to work with next, and if you interests change (after hearing faculty talks, more from other grad students, etc.) you don't want to be locked into other rotations and not get the chance to rotate with someone that you decide you want to!

I didn't set up my first rotation until about 2 weeks after arriving (and about 2 weeks before the rotation itself started) and definitely didn't set up all of my rotations at once. I really think it's program-specific though. One reason I'm really glad I waited was that my program (which is relatively large) also did a series of "mini-talks" where faculty present their current research and mingle with the incoming first years which was super helpful. Granted, there are A LOT of faculty in the program so it was a little overwhelming (though certainly not all of them gave talks) and did drag on after the first few rounds, but it was also very informative. On the other hand, it can't hurt to reach out earlier than I did, like say the summer before.
But I definitely wouldn't do it too early because you'll be wanting to set up meetings with faculty and that will be much easier when you're physically there/know your own schedule a little more, in my opinon. I guess the one caveat to this might be whether or not it's common for students to have to "compete" with each other for rotations and, if so, getting a foot in earlier than others is necessary? This was never the case for even the most popular labs in my program, but it might be a concern I suppose.
As for later rotations (however many that is for your program), my top choices definitely changed throughout the first semester from getting more familiar with the program and faculty and talking with current students and post-docs in the labs I was interested in (which I highly recommend doing before choosing a rotation!!). Both my second and third rotations were overall much better informed decisions than my first, but also went in much more surprising directions research-wise after unexpectedly hitting it off with both PIs at random department events.

The part time jobs available to you will also depend on your school's policies. Many schools in the science fields that provide a full stipend and tuition waiver might have funding that come with strings attached. Sometimes, these strings is that you must report and get approval for all "conflicts of commitment", which could include part time work, since you are expected to commit to your graduate studies full time.
 
So, you will have to ensure that your work does not interfere with your studies. Personally, it's my opinion that schools should not have strong restrictions on outside work because it's your own time. However, if taking on extra work means that you will have to take longer to finish your PhD, I can understand why schools should rightfully be concerned/prohibit this (since if they are fully funding you, they should have certain expectations of degree progress).
 
In practice, at my school, if the extra work is something like bartending or Starbucks barista, or tutoring, etc. (i.e. sometime low commitment and for extra income/fun) then it is rarely a problem. However, if the outside work is something like consulting, starting your own business, etc. then this might lead to issues. In general though, my school is supportive of grad student entrepreneurship, but they will likely ask you to take a leave of absence if you are interested in taking on a lot of outside work.

Try and find something that benefits your degree. Tutoring is a good option - it pays a high hourly rate and develops your teaching skills. I teach 2.5 hours/week and that brings in $100. Means that my stipend plus that pocket money is enough for me to rent a big 2 bedroom apartment in a major city, and support my +1.
 
Btw, don't discount big cities just because of rent. Some (often private) institutions offer more than others, and some (overlapping) institutions are based in the suburbs of big cities, which are very affordable but also bring more work opportunities downtown.