Albert Barnes Commentary Matthew 10:11

"And into whatsoever city or village ye shall enter, search out who in it is worthy; and there abide till ye go forth." — Matthew 10:11 (ASV)

Who in it is worthy. That is, whoever in it maintains a good reputation will be able and inclined to show you hospitality, and will treat you kindly. This shows that they were not to suddenly and needlessly expose themselves to insult or lack.

And there abide. This means to remain there, as Luke adds, Go not from house to house. They were to content themselves with one house; not to wander about like vagrants and beggars; not to appear to be men of idleness and fond of change; not to seem dissatisfied with the hospitality of the people; but to show that they had regular, important business; to show that they valued their time, were inclined to devote themselves to work, prayer, and meditation; and to be focused only on the mission for which He had sent them.

If ministers of the gospel are useful, it will be by not spending their time in idle chitchat and wandering about as if they had nothing to do, but in an honest and diligent use of every moment in study, prayer, preaching, and pastoral visits with their people.