Albert Barnes Commentary 1 Samuel 27:5

"And David said unto Achish, If now I have found favor in thine eyes, let them give me a place in one of the cities in the country, that I may dwell there: for why should thy servant dwell in the royal city with thee?" — 1 Samuel 27:5 (ASV)

David, with characteristic Near Eastern subtlety (Compare to 1 Samuel 21:2), suggests that his presence was burdensome and expensive to the king as a reason for leaving Gath. His real motive was to be further from observation and control, so he could act as an enemy of Saul without actually lifting his hand against him or his own countrymen of Israel.