Being attached to a university can be a big advantage if the university has good start-up support, especially since you already have a network there. However, being in the bay area can also be a huge advantage, as is free rent and food. If your university has good start-up support, and there are people in your area you want to work with, stay in Provo. If not, move out here. Another thing is that you can always move out to the bay area later. Keep in mind that moving will eat a few weeks of your time, and can be expensive.

I just moved out to the bay area a few weeks ago and I am really glad I did. If you do move out here, shoot me an email, or go to a "Hackers and Founders" meetup.