Brooklyn Bridge Park is a great place to stroll while getting killer views of the Manhattan skyline. There is also a great ice cream place nearby called Brooklyn Ice Cream Factory.
Fort Greene is a great small park that has a lot of greenery and plenty of benches to relax on a nice day. (We've also found it to be a great place to have a picnic or work on a crossword puzzle.)
Don't judge a book by its cover -- this is actually a very cool museum that we've visited in the past that has a ton of information and exhibits on the progress of the train system in NYC. It even has vintage subway cars (complete with vintage ads) that you can check out.
French Louie is one of our favorite brunch places in the area. Reservations are recommended, but not necessary.
Dekalb Market is a food hall with dozens of great dining options. It's a wonderful place to go with larger groups where everyone can choose a different cuisine and then eat together at the market tables.