Can you be a little more specific about the neighborhood you'll be in (or near/around), your preferred price range, any cuisine preferences, or whether you are looking for something fancy or if that even matters?
There are probably hundreds (thousands?) of restaurants suitable for vegetarians in Brooklyn, with some restaurants being exclusively vegan, exclusively vegetarian, or simply have some kick-ass vegetarian options.
Some of my favorite places, mostly of the super casual ilk, include:
Stir It Up - Caribbean cuisine with lots of fun and flavorful vegetarian options (i.e. "Ha Ha Chicken Balls"). Cheap and near BAM.
Papacitos - Mexican "street food" with lots of cheap veggie options. On the greasy side, and not a large restaurant, but their soyrizo is excellent.
Red Bamboo - Asian stunt meat at its deep fried best.
'sNice - salads and sandwiches.
Taco Chulo - hipster Mexican with good guac and yummy margs.
Red Hot II - More Asian stunt meat, with plenty for non-vegetarians, but better prepared than most places. Shanghai dumplings are delicious.
Farm on Adderley - if you go for lunch, their portobello mushroom sandwich is great. For dinner, their salads and apps could do the trick.
For something similar to Red Bamboo and Wild Ginger (fake meat), I also like Foodswings in Williamsburg.
Lucali if they aren't vegan for delicious pizza and fabulous atmosphere.
I've had great luck at Lunetta on Smith Street and Tempo on 5th Avenue for vegetarian options at non-vegetarian restaurants.
Chance on Smith, also not vegetarian, for "Asian Fusion" with extremely well priced lunch specials.
Many delicous and veggie-friendly breakfast/brunch choices at Cafe Luluc on Smith Street.
In the Prospect Heights area, there is Dao Palate on Flatbush Ave and Park Place. It's vegan pan-Asian, owned by the same folks as Wild Ginger.
On the opposite end of the nabe is Rawstar, a raw vegan restaurant. Located on Washington Ave and Prospect Place. Also delicious.