Mikes apartment is the perfect place to stay, if you wan't to stay in Brooklyn.
It is located in a friendly neighbourhood with cafés, restaurants and small supermarkets.
Prospect Park, Botanic Garden and the Brooklyn Museum is in walking distance. Just across the building you find the Metro Station 'Park Place' where the S train - a shuttle train takes you to 'Franklin Avenue Station', 'Botanic Garden' or 'Prospect Park', where you can switch to other Metro lines. If you don't mind walking, it's possible to walk to Brooklyn Bridge Park and cross the bride to Manhattan.
For dining I recommend Chavelas on Franklin Avenue. We also bought food from Sweet Basil, Screamer's Pizza and an Indian Place opposite the pizza place - all three places also on Franklin Avenue. On St. Marks Ave. you find a Gala Fresh Farm - a big supermarket that has everything you need.