We're visiting China for 3 weeks in late December, early January.

First 3 days we're going to see Shanghai, then 4 days in Hangzhou. Could you possibly give us advices what to see the next two weeks in a 500 km radius? We're interested in beautiful nature, hiking and history. We would prefer places that are free of charge or where the entrance fee is not very big. How cold is it normally this period? Are there many people doing hiking in winter?