I would recommend a (self-guided) walking tour of Brooklyn Heights
Lots of history and great views of Manhattan. The Fulton Ferry Landing is a good historic spot complete with Walt whitman quotes. Henry Ward Beecher preached at Pilgrim Church of the Pilgrims. Etc., etc.
http://www.southbrooklyn.net/b_heights.html

you'd probably enjoy exploring the Middle EAstern shops and restaurants on Atlantic Avenue, too

Hi guennieca,
All the areas I mentioned are safe to walk at night; of course, like anywhere else, you should always pay attention to your surroundings. If you were in Park Slope in the later evening hours, I would spring for a cab back to your inn; it wouldn't cost more than $5. You'd easily catch one on 4th Ave. If you were to walk from Park Slope to your inn in the late evening hours I would recommend walking the longest part of the stretch on Atlantic Ave, a busy street where you're sure not to be the only ones taking an evening stroll.

guennieca, the area you'll be staying in is safe at night (all the usual precautions of city life assumed), as is Park Slope. As Katie_H implied, it's the area in between that's not great: not a crime area per se, but what is a busy thoroughfare during the day (4th Ave) is pretty deserted at night, and although retail businesses are beginning to open there, it's still a primarily industrial stretch. I too would recommend a bus, cab, or subway between areas.

DUMBO gets pretty empty at night. As a long-time (female) city resident, I have to say that an empty street is always less comfortable to me than a busy one! That said, I've been out for dinner and drinks in DUMBO on many occasions and had no problem catching the F train home - it all depends on what you feel comfortable with.

Katie_H, thanks for the compliment! (You can tell where my heart lies. ;) )

Thanks for the advice! I'll take a cab at night!