SysEvo

I would personally not go to a school based on one mentor and feel like you have conditioned yourself to like school X more because it won't require sacrificing a lot and stepping out of your comfort zone. However, if you feel that the only regret you'll have by declining an offer from Penn is that it was a top program, then by all means go to school X. As a Penn student, I must say that it is definitely much more than just a top program and you'll be surrounded by a bunch of opportunities here (i.e network) , and a great environment.
You're right in that your PI has a huge impact on success, but you can't ignore the fact that the reputation of your school also has an impact. And, there are a lot of highly-recognized PIs here. Not only this, but you'll also find a lab where you fit in given that there are soooo many to choose from at Penn. 
In the end, this is only my opinion, and I urge you to choose the place that will make you the most happy; however, you should try to not bias yourself to one program just because you found ONE good fit. 

I personally wouldn't invest myself in one PI, especially if the school isn't a top program. Maybe if the school had other options in case something happened with the PI, then I would consider it. Just imagine if your PI loses funding, decides to retire, move to another university, etc. Would you be okay then? I had planned to rotate with one PI since I got to where I am, but now there is the potential that they will move to another university. Definitely didn't see that coming. Things like that you need to be aware of, even if you think it'd never affect you.

Happy to say I just accepted an offer of admission from one of my top choices and a top 20 school in my field.  For all of those with low-GPAs, there is hope! Find a masters that will accept you... do extremely well and the door will open for Ph.D programs! 
EDIT:  Also, thank you to this community for the great advice and support along the way! 

I just got accepted for the Biology MS program at Umass Boston with full funding after interviewing there a week ago. I really didn't know what to expect given that I was applying without any research experience but in the end my high GPA and GRE scores and strong letters of recommendation overcame it. Plus, my interview went extremely well. Still haven't heard back from URI or UConn, but Umass was my first choice anyways so I'll likely be accepting regardless.

Got accepted to University of Maryland's BISI Computational Biology, Bioinformatics and Genomics Ph.D program.

A potential PI just emailed me congratulating me on getting admitted into Stanford Bio, but I haven't actually heard back yet!

My application journey ended today. Very likely will choose Tri-I. Thank you guys!

Accepted to NYU with a 2.6 uGPA. Miracles happen. 

Accepted to UNC BBSP

I got accepted to Stanford for Genetics!! I thought for sure after the interview that I didn't stand a chance. Best day ever!

I don't agree with your last point. Though in the US most bio professors can't admit you directly, they can certainly give you an interview opportunity if they are really interested in you.

Got through into UC Berkeley ESPM and Minnesota EEB! Super excited 

I got mine this morning! thanks!

Accepted to UCLA IMMP !

Congrats! I received my official BBS acceptance as well today and I've accepted! Feels good to be done with this exhausting process. 

Got my official Harvard BBS GSAS letter and package today, it details how to formally accept the offer

Accepted to UPenn CAMB! 

I got mine this morning! thanks!

That's really dumb. GRE scores shouldn't matter at all by this stage. Actually, that test is a scam and should be thrown out altogether.
 

Accepted to WUSTL CSB after interview, happy to get my first choice.

First acceptance!!!
Duke Biochemistry! 

ucsd bioinformatics offer get.

I've been doing the same thing!!! Newegg and Linkedin scared me so bad!!! 
One of my programs said by the end of February. Glad it's a short month. 3 less days to panic!
 

Harvard Systems Biology admitted. 

Also accepted to Duke CMB! Now comes the hard part of deciding where I want to go...