Natick is about 13 or so miles outside boston. I went to college in waltham, which is 9 miles outside, on the framingham commuter line. I will say, recognize the difference between the T and teh commuter rail. The commuter rail comes every hour and a half, which wasn't all that convenient for me. Then, you will probably have to take the T from north station to where you want to go. We usually ended up driving into the city, which is annoying. It was probably a 20 minute drive. The good thing about waltham is that it's on the crossroads of i95 and the mass pike, so it's very easy to get around. Depending on your situation, you might want somewhere quieter and farther outside. It was nice because we had the town feel and safety, but the advantages of boston. However, if you are in the younger/single group, then definitely live in the city. If you are sticking around for a while, you can eventually move outside when you've done the city thing.
Boston is a huge college town (50 colleges in 50 sq miles), so there are lots of kids there. Lots of fun stuff to do, too, and lots of history. My biggest complaint is that the city shuts down very early. The latest T leaves at 12:30 (another reason we often drove), though they now have the 'night owl' bus until 3 or something, and bars close at like 2.
I really like boston, I would consider living there again. I got sick of the cold senior year, but the snow was nice.
Oh, I know a lot of people who live in somervile. It's pretty nice and not that expensive. Brookline is nice, but steep. Same with newton.