Places to visit Summer palace, Temple of Heaven and Nanluogu Xiang

You can take subway to those places:
To Summer Palace: take subway Subway Line 4 and get off at Beigongmen Station (Beigongmen means the North Palace Gate);
To Temple of Heaven: take subway Line 5 and get off at Tiantan Dongmen Station, Leave from Exit A and you'll find the East Gate of the Park of Temple of Heaven;
To Nanluogu Xiang: take Subway Line 5 to Beixinqiao (Exit D) or Zhangxizhong Station (Exit A), then walk westwards for about 15 minutes to the destination.
Your hotel is near to Wangfujing subway station or Tian'anmen East Station. You can go either of the two stations to take subway line 1 to Dongdan to catch subway line 5, or to Xidan to catch subway line 4.