There aren't much you can do within New York city unless you are an Artist type of person. If you like to see museum, watch Opera, or listen to music concert. There are many in New York city. I am sure you haven't gone to all yet. If you like to watch Yankee baseball game.
There are more fun for areas around New York city (within a few hours by cars.)
1. Six Flags Theme park / Safari at Jackson NJ
-
http://www.sixflags.com/greatAdventure/index.aspx.
- There are Chinatown 1 day bus trip to there.
2. Pick your own Farms
- Search it yourselves at google, there should be a lot.
- here is a useful site I found.
http://www.pickyourown.org//blueberries.htm
- Blueberries should be around the season of your time.
- I know there are "pick apple" 1 day trips from Chinatown bus tour, but if you can go yourselves with friends, there are much better choice than apple as blueberry, stawberry or peach etc. There are lots of farms offering this around upstate NY or NJ. They should be just an hour away from New York city.
3. Lake George -
http://www.lakegeorge.com/
- I already booked 2 lake front houses this June for 3 nights. My friends and I plan to bring a MahJong table and Mahjong, going to play 8-rounds in front of the lake. Of course, other activities as BBQ, fishing, rafting, swimming, and enjoying the sunshine. I will have to see if I can rent a boat to go around the lake. Lake George was some beauty, I went there with Chinatown tour before, but the tour cannot really enjoy the time there, so I am going to rent lake front house ourselves.
- There are a lot of activities around the Lake George and Adirondack park area as white water rafting and balloning. Check it out at
http://www.lakegeorge.com/Guide/LG_Activties.cfm. BTW, there is another Six Flag around Lake George.
4. Diamond mining -
http://www.herkimerdiamond.com
- haha... I found this while I was planning my Lake George trip. It sounds quite fun. Maybe I can get a couple ct of flawness diamond.
5. Golf - there are a lot of golf course does not require membership around NJ/NY. Some may have equipments for rent or for beginner. If you like to play golf, there are a lot choices.
