South Street Seaport is a fun though touristy place to visit. In the early 1800s it was a hub of activity filled with sailors and merchants. The 19th century facades have been restored now and it is a shopping and restaurant area with a bright and modern museum. At the South Street Seaport Museum you can board a red-hulled 1908 lightship, the Ambrose- kids love this treat! It's fun to walk inside the officer's cabins. You also get to board the Wavertree, an 1885 cargo ship. There are also tugboats and fishing schooners to see from a distance. It's fascinating to read the exhibits and find out about the history of this area and how it changed over time. There are some great historical photos, as well as photos about Occupy Wall Street. The building itself has a very interesting history and you can see it through the graffiti on the walls and the uneven floors. Kids will enjoy all the special activities that this area provides, including a chance to try printmaking at the 19th century printshop inside the museum. 

For $15 more per person, you can add a tugboat sail after your museum visit, offered during August. 
For a more laid-back way to enjoy this area, find a bench and just sit back and enjoy the views of the river and glimpses of the bridges of Manhattan. Have a meal at one of the restaurants or enjoy one of the bars.
A better place to hang out by the river is Brooklyn Bridge Park.

Directions

South Street Seaport Museum, 12 Fulton Street, call (212) 748-8600. Cost is $20 for adults, $14 for seniors and students, and free for children aged 8 and under.

Click on map for interactive view