I live a little under 2 miles from the campus, due west. I've been here for many years. Everyone always talks about Park Slope, but, great as it is there, it is very expensive (and honestly, the train is not direct, so your commute would be convoluted).
A great up and coming neighborhood (i.e. newish coffee houses, restaurants, wine stores, grocery stores, etc.) is the area along Cortelyou Road, between Coney Island Avenue and Ocean Avenue. If I wasn't already settled, I'd live there. Called Ditmas Park, usually. It's the area near the Q train stations at Beverly Road and Cortelyou Road. You still aren't on any direct line to Downstate, but you would be within a very short bike ride distance, or alternately, a short walk and a bus, so your commute would be around 10-15 minutes (about 1 mile). I know some of the Downstate faculty live in that area. Also, the other great thing about that neighborhood is that it is on an excellent subway line, so access to north Park Slope, Prospect Park, and on into Manhattan is easy. In the other direction, you can get to a minor league ballgame in Coney Island (go Cyclones!) in under 20 mins.
There are interesting housing options in that particular area as well. There are old Victorian mansions (not to bum you out, but think Sophie's Choice neighborhood) and some are split into apartments. It is also known as "Victorian Brooklyn" or "Victorian Flatbush". Try a craig's list search for Ditmas Park or Cortelyou Road and you will see prices on rentals.
For more info on the areas I'm talking about, this real estate agent is the local maven--she has some rentals, too:
http://www.marykaygallagher.com/
OR if you live anywhere along the B35 bus line (Church Ave) from the West Indian neighborhoods around Downstate and Flatbush to the VERY ethnically mixed neighborhood of Kensington (one of the most diverse neighborhoods in the world, I think) that would be an easy commute--Kensington has a lot to offer (not as cute as Cortelyou, but pleasant, and probably a slightly easier commute since that bus runs every 8 mins.); people who love it tend to blog about it, so you can google it and find lots of blog entries on restaurants, etc.
That's all I've got. I should get a subsidy from the Brooklyn Visitor's Bureau .