This is in response to the very first post on this thread.
Hey, I just went through this whole process last year. You have a slightly better SAT than I did, but without other "stats" like GPA and Extra Curriculars, there's no good way to judge chances. My only advice is dream big, but be sure to have realistic second option and safety schools too. Find out what you like in a school, and don't worry so much on the name. Size for me was a particularly important factor to consider. Aim for some variety too, so if you get accepted at multiple schools, you have options as opposed to "School X" and "School x". The "feel" you get for the people is usually a pretty good indicator too. Could you see yourself there for 4+ years? See if you can schedule a private chat with one of the professors of your field of interest, which most smaller private universities will be happy to set up (yes, even at Ivy League schools, and Stanford. In fact, by sheer coincidence, I had the chance to meet 1 on 1 with professors in Chemistry and Biology at Dartmouth when we visited. It was awesome). I did that, and it made a world of difference come decision time.
I applied to many schools:
Harvard, Yale, Princeton, Duke, Dartmouth, Washington University in St. Louis, U of WI Madison, U of LaCrosse, U of Eau Claire, Drake University, Creighton University, U of IA, and St. Norbert.
That was not meant to brag, just an indication that you should apply to a lot of schools with a lot of variety. I ended up being rejected from the first seven schools listed (Madison because of a clerical error on their part), though I was about as likely as most any other student to get accepted, but found that I loved Drake University, where I now study biochemistry and neuroscience. Moral of the story, don't be afraid to dream big, but remember that you should have a number of Universities you can and will fall in love with.
This is a great resource, even if some of the people tend to be elitist and dream crushers. http://talk.collegeconfidential.com/
Also, explore out of state schools extensively. Typically, only the state universities hike tuition, and can many times be as expensive for out of staters as a private school. In fact, it was cheaper for me to attend Drake University than U of IA, as Drake offered me a much fatter scholarship, and U of IA bumps the price for out of state students.