# 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 towns outside the city"

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

"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.