I live in Park Slope and love it here! tons of shopping, good highly rated restaurants, and good bars.
We also have Prospect Park, The Brooklyn Museum, The Brooklyn Botanical Garden, the main branch of the Brooklyn Public Library. On the weekends, an excellent farmers market near the Grand Army Plaza entrance to the park. If you have kids, the Prospect Park Zoo is inside the park and there is Leffert's Homestead also inside the park that kids (adults too) can take a tour of and learn about what life was like many years ago.
Here's a link to things in the park:
http://http://www.prospectpark.org/
Just walking around and checking out the brownstones could be nice. If you are a cemetery junkie like me and hubby-nearby is one of NY's oldest and most prominent cemetaries, Green-Wood. It is gorgeous inside with lakes and ducks and there are a lot of famous people buried there. There are usually guided tours on weekends, but, hubby and I just grab a map and wander around.
Here's a link:
http://www.green-wood.com/
And, as I said before, you can always walk along 7th Avenue and 5th Avenue and go shopping.