There are seldom military runways where Air Force One goes, be if U.S. or overseas. It generally uses the local commercial airports.
You are correct. As a matter of fact, depending on logistics (ie, exactly where the President is going) they’ll sometimes land at a civilian airport even though a military base with a runway is in the area. Was stationed at Malmstrom AFB, MT in the early 80’s when Reagan came to Great Falls. Since he was doing meet and greets at the other end of the city, AF1 landed at Great Falls Airport. Easier for the Secret Service to get him back and forth.