# If I have found favor in your eyes

"If I have pleased you" or "If you consider me favorably" 

# let them give me a place

"please give me a place." 

# one of the cities in the country

"one of the outlying towns" or "one of the towns outside the city"

# Why should your servant live in the royal city with you?

"I do not need to live in the city with you." or "I am not important enough to live here with you in the royal city." 

# your servant

David speaks as if he were another person to show that he respected Achish.