It's all at your fingertips! You can do anything!
This is a fantastic living history museum, great for adults and older-than-toddler kids. After your visit, walk to Russ and Daughters on Houston to pick up some bagels and whitefish, then over to DiPalos on Grand Street for cheese, olives, salami, and more cheese, then to the dollar dumpling place on Mosco for 10/$1 fried dumplings, then plant yourself in Columbus Park on Mulberry (the onetime Five Points) and people-watch while you eat delicious things.
The long history of slavery in NYC was literally unburied over the last 30 years, and this historic site and museum are the marker of that. When you're done with your visit, head north toward the Lower East Side and all of the same food recs as for the Tenement Museum.
This is where we spend our Saturdays, and it's awesome. There's so much great food, and often music, and people-watching galore, and you're right by all of Prospect Park-- one of our favorite places in the city--as well as the Brooklyn Botanic Garden and Brooklyn Museum.
Rachel was a tour guide for this company in grad school. They do great historical walking tours of neighborhoods, parks, and themes (immigration, American Revolution, etc.) in many parts of Manhattan and Brooklyn.
Gorgeous park along the Hudson, with stunning views of the Brooklyn Bridge, Manhattan skyline, and Statue of Liberty. There are lots of paths, benches, noshes, playgrounds, and piers where you can watch all sorts of sports or rent roller skates and roll around.