in Beijing:
Find out where the local parks near your hotel, and go there early in the morning. They will have everything from ballroom dancing to exercise classes (Tai Chi) going on.
It's easy to get lost on your own (the street signs are not helpful), so always carry a book of matches or some stationery from the hotel with its address. Just show it to a cab driver and he'll take you back to your hotel.
All the back streets are interesting and safe to walk.
Also the Great Wall, Summer Palace, the Ming Tombs, Tienamin Square are not to be missed but I assume these will be on your tour.
Also markets like silk alley but you will need a wide angle for those as they are very crowded. The food markets early in the morning are also bustling and interesting.
The concierge at your hotel should be able to help you find parks and markets near your hotel.

I've never been to Xian.