I live and work in Galveston. Galveston's airport doesn't handle commercial flights. William P. Hobby is the closest . It is in South Houston, 40 miles from Galveston. Houston Intercontinental is 70 miles from Galveston.
I believe Galveston Limousine Service has shuttles running all day between Galveston and the airports. Galveston's docks are located on Harborside Drive.
Hope this helps you out. We've been on the Sun Princess to Alaska and the Celebration out of Galveston. We're booked on the Splendour in December to the Panama Canal. We haven't sailed Royal Caribbean before. Can't wait!