Me too! we visited Boston over Spring Break and all the streets are like "Wheeeeeee! I can make *curves*! Watch this -- I'll join up to myself!" and also NONE OF THEM ARE NUMBERED, so you don't know how many blocks you are from somewhere.
I love the grid system.
Yep. When we went there, we were used to the New York City grid and sort of went "oh we missed the street I guess we can get back, just keep turning"--nope. But it's really nice, all the same.
For New York, I second the cheap/ good Chinatown food and the High Line. If you happen to need refreshments after walking on said elevated railroad/park in the summer heat Chelsea Market is also right nearby, with lots of food options. Central Park is also gorgeous, once you get inside past all the people hawking tours/bikes/whatever.
If you're going to the Brooklyn Bridge, the South Street Seaport might be worth checking out, especially if you like 1) history and 2) ships. My knowledge of it is pre-Hurricane Sandy, though.
....aaand, Piney already also recommended the Met
it's amazing, so I guess I'll just stop repeating what others have said.