Maybe I can shed a little light on this...
Downstate Gas Residency, consists of three hospitals, LICH, KCHC, and Downstate.
LICH - private, Cobble Hill , very nice area
KCHC and Downstate are directly across the street form one another in flatbush, which is not exactly the safest neighborhood, but you wont be spending much time walking around the neighborhood. KCHC is in the midst of a complete renovation, and their new state of the art surgical suites should be open in time for this years CA1 class.
Now there are many locations in Brooklyn that are becoming or are gentrified, Brooklyn Heights and Park Slope being the two foremost examples, residents live in one of these nieghborhoods or many other up and coming neighborhoods or even manhattan.
When in gas at downstate - you are assigned one main hospital -which your pay is based upon as each hospital pays a little differently, however just because you are assigned one hospital - you are not solely there, you may be in LICH in the morning, and the take call over night at kchc, for example.
As someone previously posted, one of the major pluses of this program is Dr. Cottrell, who everyone knows and is extrememly hooked up - residents basically get whatever fellowships they want. Other benefits, include the second largest community hospital in the country - you are bound to get good training. Plus, downstate in and of itself, has almost any fellowship you can think of - which usually go to its own residents first.
With regards to it not filling, I think a lot of it has to do with the neighborhood and part of it has to do with the program itself, leaving some spots open, if you look at Dr. A. Groganos anesthesia report, you will see he always mentions downstate as one program that could fill if it wanted to, but doesn't go out of its way to do it, why they are like this, I dont know.
Hope this helps with regards to downstate.