If you want to go to Beijing, there are plenty of schools in the Wudaokou: 五道口 area.

All of them offer pay as you go lessons and you can simply turn up

Global Village School - 地球村 http://www.thebeijinger.com/directory/Global-Village-Language-School

Sinoland

http://www.sinolandchinese.com/index1.asp

Are some of the options available

Truth be told there are a plethora of options available in Beijing and almost all of them are good up to a point.

You'll have to get a tourist visa and find a place to live yourself, although some of the schools can provide a visa if you can contact them and organise it.