First of all, that ranking can't really be taken at face value. Your degree is what you make of it. If you excel at Dartmouth, you will be a respected mathematician. Of course, a high-ranked school looks good on your resume (just like a great undergrad institution looks good on your PhD app), but it's not the only thing that matters.
The other thing you have to think about is this: What is the point? Not to get deep on you, but seriously, why do you want to get a PhD? Because you love math and you want to get a job and yadda yadda yadda...it will make you happy
. If the point is to be happy, well, why would you want to spend five years in a town you don't like or a department that's not perfect for you, when you could spent it somewhere you love and you will be happy? Five years is a long time, and if you think you will enjoy
your time at Dartmouth better than somewhere else, you should do it.
Congrats on the acceptance and the fellowship.