I ride these roads all the time, but I do it differently on weekdays v weekends. The Residence Inn airport location is good. Out the driveway, left of Main (wide bike lane) to the San Diego Creek trail. Enter the trial on the right toward the coast and follow it to the end, it will cross under Jamboree and then bear left and merge into a sidepath along Jamboree. Stay on this to Eastbluff drive and turn right staying on the side path. You will then come to back bay drive, turn right down the hill and along the bay. You will come to a stop sign at San Joaquin Hills Rd. Turn R and climb the short steep hill, cross Jamboree again and Newport Center is on the right side of San Joaquin Hills Rd. Figure out where to turn based on where you’re going.
Most of the streets have bike lanes but weekday traffic there is heavy. The route above is what I would do. On weekends I’d use Harvard, University, Easbluff Rd and Jamboree but I’d still avoid Jamboree between Main and Back Bay. Just not very pleasant compared to Harvard or the creek trail.