Back to the apartments. There are lots of really great, relatively inexpensive places to live in and around Boston, but you really do need to start looking ASAP, because the housing market is a little insane. A lot of schools have a "off campus housing" website or service where people list apartments or rooms to rent. I would check to see if your school has something similar...
Coolidge Corner is wonderful! I never lived there, but I always wanted to. It has easy access to the T, and has lots of great shops and restaurants. Ditto for Davis Square and Central Square (Cambridge). Beacon Hill is also beautiful, but it can be expensive.
If you're looking to get away from undergrads, stay away from Allston and most of Brighton (along Commonwealth Ave). I lived in an out of the way neighborhood in Brighton which was great for having a car (always found a spot, usually right in front of my apt!), but it wasn't a great location for public transportation.
If you're worried about being "had" by the broker, I think it's still possible for you to find an apartment on your own. You are looking to move "off peak", so once the just settles from the summer, there may not be as much competition for the remaining apts. You might have better luck if you are willing to have roommates and are alright with picking up on a lease already in progress (does that make sense?