My family is coming to visit Jan. 29-Feb. 4. Is this an ok time to go to Guilin and Yangshuo or is all closed?

Hi, Korey.
To be honest, it is not a good time to go there. During that time, it is cold and wet. The Li River has little water.
The parks and other attractions in the GL city are open, but the traffic to that area will be a headache for you.
If possible, it is suggested to change a time to go.

Are there any good options of places to visit during the New Years holiday in China? We'll be in Shanghai for at least a few days, but I'd rather take them somewhere else too, if I can.

Shanghai is a good choice and you can enjoy many local activities during the New Year. If possible, you can go to the Zhujiajiao Water Town where you can enjoy the New Year in the Chinese water town.