Although seeing the Temple of Heaven was great, what was even better was the park just outside the main Temple at the north end (you need to pay the entry ticket first and go through the gates, but it's before the main attraction.
We went at about 10am and there were hundreds of people excercising, doing hip hop dancing, gymnastics, Tai Chi, ribbon dancing, Bollywood dancing, playing/excercising with a Chinese bat/ball things, playing chess and checkers etc etc. Most people are over 50 years old and it's just the most incredible thing to watch. The kids just loved it and even joined in on some of the fun.
If you go there, don't miss this. It gives some great insight into the "everyday" culture and lives of the people.
Also, if you don't mind eating street food, at the entrance/exit of the south gate in the little alley, there is a noodle "shop" with excellent noodles. You can watch the guy making noodles by hand (kids loved it) and then you get to eat it. - 10 CNY a bowl. Right next to him is a lady making handmade bread with chicken inside - delicious. We called them "Chinese burgers" 5 CNY each. You sit on tables out in the street. Our kids loved it and thought it was one of the best meals we had - noodles were exellent since they were so hot and the day we had them was a freezing cold day!
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