Here are some tips for fun and free things for visitors to Beijing to do:

1. Make a list of weirdly-named dishes found on restaurant menus
Menus in top Western restaurants will be error-free, but not as much fun as those found in neighborhood restaurants where the menu may have been translated by someone with limited English. How about a bowl of “three fried things?” A plate of “three odd fellows” certainly has possibilities. Many restaurants these days provide picture menus with the English translation below the dish’s picture. This cuts a lot of mystery out, but lets diners see what they’ll be eating.
2. Work out on street “gyms”
No time for a workout at the gym? Not to worry. There’s exercise equipment located throughout Beijing’s residential areas. The Beijing government put the equipment there in an effort to stem growing obesity among its citizens. The equipment is pretty basic, but gets the job of working off last night’s Peking duck dinner done. Two good areas to look for the exercise equipment are between the Drum and Bell towers on Gulou Dajie, and along the east side of Houhai Lake. There’s even a ping pong table there, but paddles and balls are not provided.

3.Take a walk
Not only is walking good exercise, but it allows visitors to get up close and personal with Beijing. Good places to walk and people watch are Tian’anmen Square and the Olympic Green (there are charges to tour the Bird’s Nest and Water Cube, however). Take a leisurely stroll along Houhai Lake and the lakes north, with detours to explore what’s left of the hutongs. Hutongs are quaint residential neighborhoods which are falling prey to the wrecking ball as Beijing rushes to modernize.

There are a lot of things for free to do in Beijing. If you take your attention to notice while travelling in Beijing, you will see.
Shanghai:
1. Ancient culture: Shanghai museum
The Shanghai Museum is one of mainland China’s best collections of treasures. With four floors to explore, you can easily spend half a day or more learning about Chinese culture as you browse through bronzes, jades, calligraphy and porcelain (to name a few). There is also a wonderful book/gift store (free to enter) and a good audio tour (inexpensive).
Address: officially #201 Renmin Avenue, Shanghai. Practically speaking, it’s on the southern end of People’s Square.

Opening Hours: daily 9am-5pm

2. Art: M50 Moganshan Road contemporary art galleries

M50 is the name of the complex that has become the Moganshan Road Art District in Shanghai. Formerly a set of dilapidated warehouses, the complex, just south of Shanghai’s Suzhou Creek, has been turned into the premier location for Shanghai’s modern art movement. Take a nice stroll around and look at what China’s contemporary artists are up to.

Address: 50 Moganshan Road near Suzhou Creek.

Opening Hours: daily (approximately) 10am-6pm

3. Shanghai parks

Most of Shanghai’s parks don’t charge an entry fee (some do, usually between 5-20rmb). Parks are a wonderful way to observe and even participate in Chinese culture. Folks head to parks early to exercise and walk. Kids play and grannies walk hand in hand while minding children. You’ll usually encounter a group of oldies singing or dancing and you may even be asked to join. Bring a badminton set and hit the shuttlecock back and forth, you’ll definitely attract some attention and probably a challenge match – but watch out, the locals are good!

4. Free Shows

Free shows in Shanghai come and go. The best way to get information is to pick up a copy of one of the great (and also free) English-language magazines at bars, restaurants, shops, and cafés around Shanghai.

Shuffle Bar is a dark, bare bones kind of bar, but it’s actually one of Shanghai’s better music venues. You might have to pay a cover charge on some nights, but on others you can check out all kinds of music—from blues to punk—for absolutely nothing.

Tanghui has an open-mike night on Wednesday from 9 PM on where all kinds of music are welcome.