What I remember about tai chi was that no one wore special clothing and there was no leader. People would just stop and join in. They didn't care if strangers joined in - several of our group got up early every morning to go do tai chi with the neighborhood folks. We also eschewed the hotel breakfast (incredibly awful) and went out to eat street food with the neighbors. We had some good street food, and it was fun to interact with the folks, using sign language mostly. They laughed at us a lot, but were also really interested in where we came from and why we were there.
I remember eating mutton kabobs in the muslim neighborhood where we were training in Beijing, cooking them ourselves over the little grill. And some wonderful bread cooked on the spot, stuffed with onions. And a sort of pancake or crepe with an egg cooked on it and something that tasted like hoisin sauce. It was fun to watch the vendor pour out the batter, spread it quickly into an incredibly thin pancake, flip it, crack an egg and cook the egg on the crepe all in less than a minute. There were neighborhood soup vendors -- we went to a local market and bought our own metal bowls and plastic spoons for the soup. Much more fun than eating so-called western food at the hotel.