Dedi

I LOVE my advisor. I interviewed her while she was interviewing me, and the interview began with my first email. Over the last few years, this has been my experience:
- She replies to emails within hours
- She works on my manuscripts/proposals/research needs 7 days a week & gets me draft comments back within 2-3 days. 
- If she will be out of town, she lets me know months in advance
- She allows me to reach for the stars, as long as she thinks it is feasible
- She is super focused on my career advancement and encourages me to think holistically when I take on any new responsibilities. 
- She will put her foot down if I am fucking up (which is never for me, but she has done it to peers)
- She never has more than 7 graduate students at a time that she is mentoring
- She understands that not all graduate students are created equal and mentors all her students differently according to their personalities/needs
- She is demanding and engaged and encouraging
- She is well known and respected in her field. 
 
This list could go on. I am 4 years in and I still LOVE her. I uncovered most of these traits by asking pointed questions during our email correspondence and during our interview. I also contacted her current graduate students for information. I hit the advisor jackpot. 

I have an excellent advisor.

-He makes time to meet with me, and encourages a regular schedule of meeting.  We meet formally every two weeks but also communicate via email.

-He's flexible - we've met over Skype when I was away at conferences or visiting family, or when he had to be away.

-He's managed to balance allowing my independence while giving good guidance, and at different parts of my career.  He guided me much more in the beginning, but now that I am finishing up I do much more of the guiding of our relationship and he functions more like a support system.

-When I got burned out and discussed leaving the program, he remained calm and tried his best to help me deal psychologically.  He was a big factor in actually getting me to stay.

-He gives me really good feedback on my papers and drafts...although not always...prompt.  (However, I have adjusted for this and just try to leave some flexibility/extra time for him to look at my stuff.  Honestly, every advisor has flaws, and this is a tiny one in the large scheme of things.)

-He looks out for my career; he recommends experiences and postdocs and programs; he introduces me to people.  On the flip side, he allows me a lot of independence, and I have largely been able to choose what I want to work on, how much, and how intensely.

-He's just a genuinely nice person.  He encourages me to take time off, asks about my husband, and we chat for a little while about our personal frustrations.  He's had the lab over to his apartment for a party and comes out for drinks and dinner every now and then.  He even brought ice cream bars to lab meeting for my birthday once

Before I chose him to be my advisor we had a conversation that I used to gauge our working styles.  Part of what a good advisor is is consistent from student to student.  You need someone who will give you good feedback - both positive and critical when necessary.  You need someone who will read your drafts in more or less a timely manner.  You need someone who uses positive reinforcement more than any other technique of teaching.  Someone who knows how to strike a good balance between independence and guidance, and someone who is genuinely interested in your career and helping you become better.  You don't want someone who just needs an RA to be a grunt worker, who doesn't seem interested in you or your career, or who's going to micromanage your every move.  You don't need anyone who's never going to look at your work.  But you also don't want anyone who's always going be positive and never criticize you or push you to get better.  You need someone to tell you the hard stuff.

But some things are very personal.  I am highly independent; I like to manage my own time, and I don't want anyone else wanting me to account for hours or anything like that.  I think I would resent working for a professor who wanted that.  However, some people like being a little more managed.  I also don't want anyone telling me what projects to pick up; I can select my own projects, and mostly need someone to bounce ideas off or help me shape them a bit.  But some people prefer that their professors guide them to projects (at least in the beginning) or assign them something to work on.

You can find these things out - some of them - in a conversation.  I went to lunch with my advisor when I was admitted and we basically talked about working styles and his expectations and all that stuff, and it seemed that we were quite compatible both research-interest-wise and personality-wise.
 
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I agree, though that there's nothing inherently terrible about telling someone they are not well-suited for graduate school.  Some people simply are not, and a GOOD advisor tells you when you aren't well-suited for a pursuit rather than let you do it and flounder/flail.  And although an advisor should be overall supportive, I also agree with the above that they are not supposed to be unconditionally supportive.  If you do bad work, or they think that you are going into a research area that will not get you a job, a GOOD mentor will tell you that so you can fix the problem.
 
You may want to check out this book: Getting Mentored in Graduate School.  It's geared towards helping grad students select good advisors/mentors.

My advice (even though you've already decided) is to consider the amount of independence you have with the research project. Will you be creating the methodology? Will you be writing the proposal? Will you analyze and interpret the results? Getting a paper published in a prestigious journal wouldn't be the point, but rather the experience that can be added to the SOP (which I believe is still important). I feel that you would probably have more independence at your home institution, so I don't need to convince you otherwise.

My advice to you is to not think about the motive of getting recommendation letters. In my opinion, it can make professor-student relations seem a bit forced and not genuine. I am a shy student myself, and sometimes I can feel my heart pounding in anxiety before I go to a professor's office (or it could be the three flights of steps...), but once I go there and start chatting the anxiety goes away. I regularly send my professors articles of interest to discuss, especially if they're new and relevant to the topic we are on. I also go to office hours to discuss certain matters (whether they are academic or not). You need to be comfortable with your professors and let the relationship go where it wants to go. Don't feel rushed; you have almost a year to establish something with a few of your professors.
As long as you do well in class, I don't see why the professor would be reluctant to talk with you. However, I come from a private liberal arts college, so my view might be different from what the large university subculture is like.

I hate to say it but since you got 3 interviews out of 4 applications, I don't think this is about your application packet. Clearly, your application was intriguing enough for these schools to want to interview you. That would indicate (I think) that you are good enough to get your foot in the door, and that all these schools were considering admitting you despite the weaknesses that you list above. The fact that all of the rejections came post-interview make me think that perhaps you didn't handle the interviews well. It's hard to guess what the issue might have been without knowing more, though. My first guess would be that since you say you have less experience in the field you are apply to, that this was a concern for the schools; maybe you didn't do a good enough job convincing them that you know enough about the field or that you'd make a good candidate for it? Maybe they had concerns about your grades that you somehow failed to assuage? These are pure guesses, of course. 
 
Also, I would not recommend applying to schools that you don't want to go to. What's the point? Actually, this makes me wonder if the problem with your application this year was the fit, and that it became clear during the interviews. As an applicant from another field, you want to demonstrate that you understand how the new field works, that you can define a reasonable (in scope, feasibility) research question(s), and that you know what schools are good places to study that question (and why). Perhaps that didn't come through as clearly as you'd hope. The fact that you only applied to 4 schools and are already talking about applying to ill-fitting schools makes me think that perhaps you could have done a better job researching programs to find ones that really fit what you want to study. I would be willing to bet that there are more than just a handful throughout the country. So maybe the problem was in your ability to communicate why you chose the schools you did? (But, of course, this is another guess.) 
 
ETA: In addition to these guesses, it's worth noting that sometimes it's really not about you. There are more good applicants than spots in good programs, so you could have done everything right and still drawn the short stick. There is not much to do about this situation except try again, and in the meanwhile get more experience and perhaps apply more broadly next time.