One photography suggestion...just behind the Forbidden City there's a park on a hill (I think there's a very small entrance fee) that has a great view down into the Forbidden City.
If you like interesting architecture (for photographing or just looking at), take the subway to the Olympic area, which has some extremely cool buildings (especially the "bird's nest" stadium & the "bubble" swimming hall). I don't know whether you can go inside any of them - I just wandered around the outside.
If you like people-watching, go to some of the big parks (there are several along a string of lakes west & north of the Forbidden City), where there are groups of local people doing various things (tai chi, ballroom dancing, some sports involving small balls, artistic banner-swirling, small music & dance performances, etc.) that are interesting to watch and perhaps photograph.
And don't miss an excursion to see the Great Wall if you can - a couple of the more popular sections closer to the city are (from what I hear) crowded tourist traps, but the Simatai section was uncrowded and authentic-feeling when I was there a couple of years ago, and though it was farther away, a fast highway had recently opened which made it not too long to get there. You'll probably need to hire a car & driver to take you there, however - not sure, worth some research, but probably.
Lisa