Anyone interested in Brooklyn (Morris ) I lived there for 5 years and I'd recommend splitting it into sections
1) DUMBO / Brooklyn heights
Take the subway to either Clark St or York St. From here you can see all of Dumbo which has all the renovated warehouses (bit like Shad Thames in London) the renovated antique horse carousel and the infamous grimaldis pizza (altho its NOT worth the queue) Under the bridge there's a great smaller kids park, plus its a huge area for official wedding photos etc so you can often do some v interesting ppl spotting as the outfits are often very OTT!
Brooklyn Bridge park is awesome and keeps being extended. they have lots of outdoor sports rinks there, including an ice rink in the water, kayaking etc. There's volleyball courts, bike path (you can rent bikes like boris bikes in London) and a nice bar down by the volleyball. In the summer you can also take the free ferry from here to governors island, which is a converted naval base which is all pedestrianized
From DUMBO you can walk up onto the promenade to Brooklyn Heights. Worth a trip for the architecture - its the neighborhood wealthy traders first settled in and it has tons of old house and carriage houses. You get a really good view of the statue of liberty from here
From here you can walk or get the subway to Caroll Gardens (old mainly Italian neighborhood which has now gentrified) and Bergen St. Lots of nice small independent bars, shops and restaurants round here
2) From Carroll Gardens its a quick ride to Park Slope. (you could probably do 1 and 2 in a day if you have the stamina) very residential and lots of change going on so unfortunately lots of small business are losing their leases. However, nice bars etc there and only a 15 min was from Prospect Park which is like central park but smaller and more 'doable' Next to the Park there's the Brooklyn Museum and the Botanical Garden
3) Williamsburg - originally full of hipsters and relatively edgy (by NYC standards) not so much now but still retains an independent feel. Good bar and music scene, and I can massively recommend the Brooklyn Brewery for a stop off. You can do tastings by buying beer tokens and taste all their regular and one off brews. Lots of ppl have been priced out to Bushwick which is worth a wander through altho again quite residential
Brunch is huge in all the above places and restaurants turn over owners etc quite quickly so its worth researching the latest places on line