I may have a slightly different perspective on this question. I went to a small college with a small CS department. It doesn't show up on any of the lists of prestigious institutions and most people probably haven't heard of it. Even so, I managed to learn a great deal both in class and on my own. Coming out of college I was able to get a nice job based on the skills I had acquired and I’ve continued to move forward ever since. In career terms, you’ll probably advance more quickly if you go to Stanford or MIT, but please don’t get the impression that those are the only ways forward. By the same token, there are wonderful opportunities for learning about interesting subjects at those kinds of schools, but computer science is a constantly evolving field and knowing how to teach yourself will be tremendously useful in the future.
My advice is: look at the other answers to this question for good suggestions to aspire to, but never get discouraged if you don’t end up there. There has rarely been a more democratized subject than computer science and while it is by no means easy, if you have an internet connection, curiosity, and patience, it’s within your reach.