The whole program is just short of 4 weeks. There's some travel time in there to get between points, but I don't know quite how much, nor how we're getting around. Just to clarify, this is a program run by a US university. We'll be traveling with a couple faculty, so this isn't the sort of thing where I can really take off on my own. Unfortunately, I'm also limited on my arrival and departure dates, so I don't really have time to go elsewhere (like HKG).
I don't think going to Tibet is on our itinerary, although we may be going to the plateau. Our time in Beijing includes the Forbidden City, Great Wall, Ming Tombs, Tiananmen Square, and a few other places. I also have a couple half-days of free time there. I don't know about the rest of the trip yet.
I realize I don't have a lot of info right now, and I can ask again when I do have more details. The main thing I'm looking for is points of interest for the periods when I do have some free time.

Thanks for the help, Jamoldo.