"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".
"Live with local residents" emphasizes the act of sharing living space with locals, which can imply a deeper cultural and social integration.
"Stay at a local resident's home" focuses more on the physical location of accommodation, highlighting that one is residing in the home of a local person.
Both expressions are accurate and can be used depending on the context and the level of detail you wish to convey.