stay at a hotel泊まって is the te-form of 泊まる, meaning to stay overnight. It can connect to another action or be followed by いる to describe an ongoing stay.
JA: 旅行中は駅前のホテルに泊まって、毎朝歩いて観光しました。
EN: During the trip, I stayed at a hotel near the station and went sightseeing on foot every morning.