This park, with Pier 1 and other scenic spots, offers relaxing, riverside strolls with ample greenery and fantastic views of Manhattan.
Tourists and locals alike enjoy it, and not everyone seems to know about it. Nice way to spend an hour or two, walking, reading under some shade on a bench, or taking the kids.
http://www.brooklynbridgepark.org/
The area appears relatively safe, too, as I saw all ages there. But remember, it's still NYC, and with such a big city one must always be vigilant.
Cheers, Brendan