Not many different universities. Just two. My school has a party school image and because of curving, it's a very easy A, so the education is not respected. If I take summer pre-med or maybe non-pre-med classes elsewhere, like Stanford or Princeton, then that means I have proven myself against Princeton and Stanford students, right?
If you are so concerned with your UG's reputation, then you should transfer. Otherwise, polarbare50 is right: you are doing yourself an injustice taking your premed courses elsewhere. Furthermore, summer classes tend to have a reputation for covering less material...which doesn't help your argument either. Focus on learning the material, getting the grade, and building your reputation. If you want to take a class somewhere else, then take something that's not offered at your institution.
Also, if you want to get into a MSTP, you should understand that Gen. Chem., or any other prereq., is not going to be a deal breaker for you. What matters is research!! While a high GPA and high MCAT scores are expected, MSTP care most that you have significant research experience under your belt. If your party school is filled with slackers, then all the better for you. This will give you the opp to stand out to your professors, which will become your gateway into their labs. If you don't take Gen. Chem. with them, and subsequently "blow their socks off", then how do you plan to prove yourself to them?? Ace your classes, show interest, and start doing research!!! You should have at least two solid years of research before applying. Lastly, spend your summers doing something valuable, like research! You can do summer research anywhere....so that's a good time to see if Stanford has a program.
Lastly, if you want to "prove" yourself: Consider taking the Calc-based Physics series if you haven't already. It'll help prepare you a 'bit' more for Physical Chemistry, which I'm assuming that you'll be taking. On that note: I'd also take diff. equations, linear algebra, and mathematical programming. Those three will give you a great mathematical foundation for a science PhD program, help a 'bit more' with PChem, and also help demonstrate that you're not just some drunken hippie kid lookin' for your free ride. Peace.