US Citizens living abroad traveling back to New York with overnight stay in Shanghai.

My family is American and we have been living in Taiwan. My son and I will be flying Taiwan-Shanghai-New York this summer round trip on China Eastern Airlines to visit family and then returning to Taiwan via Shanghai as well. We have overnight layovers in Shanghai both directions and would like to stay in a hotel to get a good night's sleep before flying the next morning. Can we do this legally and what do we need to know or do before arriving there? Does this count as the free landing visa, and do we need to fill out any paperwork or go to a special office upon our arrival to Shanghai, Pudong International Airport? We plan to stay at a hotel near the airport. Thanks for helping.