This is pretty much how I am looking at it. My undergrad research advisor, who herself went to Columbia, went as far as to say that once you get out of the top 20, rank doesn't mean a whole heck of a lot. She also said that it doesn't matter between #9 and # 12, because the rankings do shift, but like you said, the schools tend to stay in the same bracket of 10-15 ish.
The way I am going about it, I applied to 3 top 20 school and as long as I got one of them I would go because it was in the best interest for my career (unless of course I hated it when I visit). Outside of them, I choose schools based on the geographic region, school and department size, research, etc. Not all schools are even ranked, so if they are ranked they are a good school. I was told it doesn't really make much of difference if you go to a number 50 or number 70 school.
So all in all, wait until you get all your acceptances to decide, and VISIT THE SCHOOLS. You may find that you visit a top school, and you just don't like the feel atmosphere of the department. If you were accepted, you are in. You have the spot until April 15th, so take your time.