If you're interested in doing tai chi or seeing how locals do it, it's best to visit any park in the city between 6:30 and 8:30 in the morning. Originally a martial art, today tai chi has become a very popular relaxation technique for millions of Chinese throughout the world. The movements are especially slow and effortless, seeking a body-mind balance to arrive at a meditative state.
If you were hoping to take a class, you might be out of luck, since courses usually last for several weeks. Still, you can always blend in discreetly and try imitating the movements!