Mullane's bar and grill on Lafayette may be your best bet.
Dekalb Market or Junior's if you don't mind walking a little further.
Unless bbq isn't too spicy for you, in which case I'd recommend The Smoke Joint.
Directly across form the BAM Opera House there has been, for many years now, a series of different restaurants, all either Austrian and German. At one time the place was quite nice, now it's called The Black Forest. I haven't been there.
There used to be a good Italian place on Fulton called Scopello but it closed, a victim of the rising rents in the neighborhood.
Deniz, a Turkish restaurant very close to BAM, is very good, but like so many of the good nearby restaurants, is "ethnic."
If you don't mind going further into Fort Greene there are many good restaurants, including several French bistros; the neighborhood has a lot of recent immigrants from France. And the quarter of Park Slope nearest to BAM has many good restaurants. I'd highly recommend Convivium, for instance, which is only about five blocks from BAM, but it's only open for dinner.