Several from my class lived in Sunset Park. You could get to Downstate from the Latino part of the neighborhood on the B35. From the Chinatown part you'd either need to drive or do a sort-of-long train ride. Though, the N is express to Atlantic for the 5 express to Downstate, and plenty of people (including plenty in Park Slope) have commutes that long.
One Chinese guy also drove from Flushing everyday, and the longest commute I heard of was the LIRR in from the Island everyday to the subway at Atlantic. I wouldn't overblow the importance of being near campus.
Prospect Heights proper (west of Washington Ave) is somewhat recently gentrified and nowadays offers some of the best of Brooklyn at a price to match, if maybe a touch below Park Slope and Brooklyn Heights. Generally convenient to Downstate on the 2.
Crown Heights is where most of the apartments advertised as Prospect Heights actually reside, as NYC realtors get tend to get creative with the boundaries of rich neighborhoods to include adjacent poorer neighborhoods. You may even see "ProCro" thrown out there to try to cross-sell the western part of the neighborhood. Historically split between somewhat insular Lubavitch Jewish community and West Indian community. Convenient to Downstate at the Franklin Ave stop - this area historically Caribbean, currently experiencing a big white yuppie influx as places like Prospect Heights become unaffordable to most. (see ilovefranklinave.blogspot.com)
Park Slope gentrified in the 1970s, now one of the most notoriously bougie liberal neighborhoods in the country. A lot of fancy bars/cafes and people that bring their babies in expensive strollers to same. Convenient to Downstate if near the 2 train. Many students live here even if their commute's not the best because it's so nice. Priced as you'd expect. Ranked #1 in this Nymag comprehensive NYC neighborhood listing:
http://nymag.com/realestate/neighborhoods/2010/65374/