I always like hiring a local guide at tour sites when they're available. These are people who you can hire (sometimes you need to buy their ticket as well -- it depends on the site) who will accompany you through the site as a personal guide. Costs vary, but it usually isn't very expensive.

The nice thing about this is that the people running the tours are targeting Chinese guests so don't tend to have the sort of misconceptions about foreigners that can be offputting when you just want to enjoy your vacation. Also, they're knowledgeable about the site and that gives something natural for you to talk about. So it is easy to have a language lesson that doesn't feel at all like a language lesson, and it is easy to ask for clarification about things you don't catch the first time since their job is to answer your questions.

Best experience was at the Terracotta Warriors in Xi'an. I also had a good experience at the old City Wall there.