"在当地居民家居住" can be translated into English as "live with local residents" or "stay at a local resident's home". Both expressions convey the idea of residing in the home of a local person. Here are example sentences for each:
1、 "During my trip, I chose to live with local residents to experience the authentic local culture."
(旅行期间，我选择在当地居民家居住，以体验地道的当地文化。)
2、 "I had the opportunity to stay at a local resident's home and learn about their daily life."
(我有机会在当地居民家居住，并了解他们的日常生活。)