Which summer internship to take? I asked a similar question last year, but the stakes have changed slightly.

So, I have an offer from a top 5 program in Chemical engineering (my major). There are a couple of extremely accomplished professors in fluid mechanics here, which is what I want to study in grad school. However, I am not so interested in attending this school for graduate school because it does not send many people to academia post-graduation, despite being a top 5 program, mostly because it isn't a very big name school. Or at least I assume this is the reason.

The deadline to reply to this school is March 5th. 

To complicate things, I am waiting on a reply from a much more prestigious university for a summer internship. While the school has a much better name, its ranking is slightly less (number 6 for chemical engineering). I think I have a very good chance of getting this internship (my PI went to grad school here and wrote a very strong letter, plus I have a good resume otherwise). However, I learned today that they will NOT be able to get a response back to me before March 5th.

I am much more interested in attending School 2 (slightly lower rank, better name), because they very frequently send people to academia, which is my long term goal.

School 1 (higher rank, worse name) was pretty firm in the March 5th date, so I don't think I can ask for an extension.

Financially, School 1 offered me a slightly better deal, I'd be netting about 2k more over 10 weeks. However, that isn't as important to me, since the experience is worth far more than the money.

I apologize for the long question, but any advice or guidance would be appreciated. Am I putting too much emphasis on the name and rank? I don't want to be greedy and put all of my eggs in School 2's basket, and be left with nothing if I end up not getting it after all.
Since these are both REUs, I do not think attending school 1's summer program will affect your chances of attending grad school and continuing in academia.  Most REUs are designed to give students an opportunity to see if they can conduct scientific research and / or enjoy it.  Depending on the university and the discipline, they may be considered 'recruiting' camps for people to attend that university's grad school program in your discipline.

Since you have a fairly strong inclination to working in academia, you do not need the experience other than to confirm your suspicions and to make you a better candidate when you apply to graduate schools.

As for what I would suggest --- ask when you think the earliest day / time you would be able to get a response from School 2 on acceptance or rejection, and then from there, try to see if you can eke out some more time on School 1's deadline so that you don't end up shooting yourself in the foot.

You may also be able to talk with your current PI and see if he can hear anything through some back channels as to whether or not you have a decent chance.

At the end of the day, it's up to you.  Consider all your options wisely.