You'll enjoy the mountain views and monuments in Shuangqiao District. You might want to make time for a stop at Bishu Shanzhuang or Chengde Mountain Resort.
If you're a traveller that's interested in mountain views, Shuangluan District might be a good pick.
If you're spending some time in Yingshouyingzi Mining District, Wulingshan Forest Park is a top sight worth visiting.