Hello!

We would like to travel for about two weeks some time between middle of January and February. Currently living in Beijing, so it is really cold and we would like to go somewhere warm.
1) Are there any places you could advise? We thought about going to Yunnan, but heard that it gets really cold there as well?
2) Just wondering: I am currently holding a chinese residence permit. If I wanted to visit Taiwan, would there be any problems?

thank you very much and happy new year!