A college degree is not a sign that one is a finished product but an indication a person is prepared for life. (Edward Malloy)
Going to college is a major event in one’s education, but the choice of exactly which college to go to is not as critical as it is sometimes portrayed to be; usually, there will be several good choices that suit your specific strengths and weaknesses, and it is not absolutely necessary to secure the “best” choice for your undergraduate or graduate education. I would recommend a flexible attitude towards this decision; by focusing too much on one institution, you might overlook others which may in fact be a better fit for you.
It is common to focus on the general prestige of the institution, but actually it is the specific strengths of an institution which should play a more important role in your decisions. Examples of specific strengths include particular research strengths, teaching programs or initiatives, campus resources, academic culture, location, flexibility, affordability, availability of financial assistance, and so forth. On the other hand, given that your interests or situation may change somewhat as you learn more about your chosen field, one should not be too narrowly focused in one’s selection criteria; for instance, if you wish to go to an institution purely because of a single faculty member there, then you might run the risk that that faculty member moves, or is no longer accepting students.
I do however strongly urge that you study at different places; it’s good to move a little bit out of your own “comfort zone” and broaden your education. It’s also good to talk to your advisor about these matters.
My final advice is to have no regrets once one has made one’s choice; get the most out of the place one has chosen, and don’t spend too much time worrying about whether the grass would have been greener elsewhere. In particular, I would not recommend trying to “have the best of both worlds” by somehow trying to study simultaneously at your two top choices; this is very complicated to execute and usually does not work out very well.
I myself earned my undergraduate degree at Flinders University in my hometown of Adelaide, Australia – a small and not widely known institution, but one which was very friendly, close to home, and whose maths department was willing to accommodate my unusual educational experience. My graduate degree was at (the somewhat better known) Princeton University, which turned out to be a good fit for me, as I ended up with an excellent advisor and a challenging, self-driven environment which shook up my complacency about my own mathematical knowledge. My first postdoctoral position was at UCLA, which I liked so much that I have stayed here ever since, even though some of the faculty that I originally came to UCLA to work with have since left. Of course, there are many other good schools, which each have their own strengths and weaknesses. (For example, if the activity of big-city life is important to you, then Princeton does not fare terribly well in this regard.)