Cheap clean swimming pools do exist outside of expensive hotels. Here is a list of some of Beijing's best public swimming pools:

Friendship Hotel
Friendship Hotel, Baishiqiao Road, Haidian District
6849-8888, 10 am-11 pm, ¥30/2 hours

Fragrant Hills Hotel
Fragrant Hills Park, Haidian District
6259-1166 x 3243, 10 am-1 am, ¥30

Sino-Japanese Youth Exchange Center Swimming Pool
40 Liangmaqiao Road, Chaoyang District
6466-3311 ext. 3185, 1-9:45 pm, ¥50

Dongdan Swimming Pool
A-2 Dahua Road, Dongdan, Dongcheng District
6523-1241, 10 am-10 pm, ¥30

Overseas Chinese Village Swimming Gymnasium
Inside Overseas Chinese Village, Jianwai Avenue, Chaoyang District
6515-0615, 10 am-8 pm, ¥50

Tiantan Swimming Pool Gymnasium
4 Tiantan East Road, Chongwen District
6701-7562, 12 pm-1:30 pm, 7:45-9:15 pm, ¥10

Yingdong Swimming Pool
Inside Olympic Stadium, Chaoyang District
6491-0468, 11 am-11 pm, ¥30