does person holding USA passport need visa for this itinerary

On October 24 we are arriving at XIY (Xian airport) evening and departing from Xian via bullet train to Shanghai within 24 hours. We will then depart Shanghai via cruise within 48 hours. So our stay upon landing at XIY and departing Shanghai port will be less than 72 hours. Please advise if entry permit is necessary and which to get.

38 hours later we will dock at Tiajin via cruise ship but are planning a land tour with a 1 or 2 night stay in Beijing. Departing Tianjin within 60 hours of arrival. I'm pretty sure no visa needed here but please advise.