Of all the parts of Brooklyn I've seen so far, my favorite is the Park Slope area where I live. From there, you can visit Prospect Park, the Brooklyn Museum, and my apartment. And probably many other things that even I haven't seen yet.
Quick Tips: If you're in Park Slope, 5th avenue and 7th avenue are good places to stroll. There are lots of cafes, restaurants, and people walking dogs.
Best Way To Get Around: The subway goes all over Brooklyn. The F line and the 2/3 lines and some others, apparently, will take you right into Park Slope... and beyond, if you're not paying attention. I don't drive here, but parking doesn't appear to be easy to find.