Tibet is the main place that comes to mind -- you need a special permit to go there. (Most foreigners, even those living here, use groups to go to Tibet in order to cut out some of the bureaucracy, but in many such cases it's almost expected that you're going to ditch the group during your travels.) In the past, the PRC has also tried to keep foreigners out of certain impoverished areas, like Gansu province, because they don't want the word to get out that China isn't all hunky-dory. But, I don't think this is so much the case any more, so if you're dying to check out Gansu, you can probably do so. In general, it's pretty easy to get around these days -- you'll run into decent English speakers just about everywhere.

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Are there any published travel guides anyone can recommend? Thanks for the previous responses!

Lonely Planet is regarded by many as the bible. It's only drawbacks are that it's a bit outdated now (the same goes for the rest) and that it still tends to target the budget demographic. Let's Go is okay and Fodors is useless. Lots of people in the Bay Area have extra LPs laying around -- I could even lend you one if you want.

I also suggest that you get maps to each city you visit (the freebies that hotels hand out are just fine and are bilingual). Since most Chinese cities are pretty logical in their layouts, it's almost impossible to get taken for a ride if you know where you are and where you're going, even when you can't speak a word to the cabbie.