Lower East Side

Economy Candy - Candy store with obscure and hard to find candy
108 Rivington Street, 10002

Tenement Museum - Shows what housing was like for many immigrants in NYC 100 years ago
108 Orchard Street, 10002

Teany - Vegetarian/Vegan friendly restaurant and cafe owned by Moby
90 Rivington Street, 10002

• Fly a kite
• Perform the Beat it dance (hahaha)
  

Bronx

*The New York Botanical Garden

*City Island

The Melting Pot on a High Boil in Flushing

Flushing, Queens

Governor's Island

Official Link

Wikipedia: Governor's Island

The Island is open every Friday, Saturday and Sunday until October 12th. On Fridays, the Island is open from 10 AM to 5 PM. On Saturdays and Sundays, visitors are welcome from 10 AM to 7 PM.

Accessible by ferry at the Battery Maritime Building

• House tours (?)
  
• Weekly events (check website calendar)
  

Red Hook, Brooklyn

Wikipedia entry: Red Hook

Map of Red Hook with pictures and descriptions located here

Serviced by the B61 bus

• Food vendors at ball fields
• Piers
• Ikea
  

Ditmas Park, Brooklyn

http://tinyurl.com/ditmaspark

From Wikipedia

Ditmas Park is a neighborhood in the New York City borough of Brooklyn, and is one of three Flatbush neighborhoods which have been officially designated a Historic District. Located on land that remained rural until the early 20th century, the neighborhood consists of many large, free-standing Victorian homes built in the 1900s.

Also, we can try to track down this in the neighborhood