As a regular visitor to NYC, I can only echo the comments that 8 days is starting to get a bit much. That said, if you were to rent a car for a couple of days the drive north into the Hudson valley is beautiful. Also, you might look to use your Metrocard on the city's ferry network which a lot of tourists ignore. For the same price as a subway run, you can travel along the East River, and then down as far as Rockaway, which on a sunny day is a lovely way to spend the afternoon. 34th St ferry terminal is ideal to pick up various routes over to Dumbo, Williamsburg, and all points nth and sth.

DC - a terrific place and all the various options of the Smithsonian museums, plus the nightlife of Georgetown makes it an ideal place to spend a few days. But yeah, hot and humid in July.