Since the ocean will be directly on your left for most of the drive, surf fishing would be a great way to enjoy the beach and fly fishing at the same time.
A good friend turned me onto fly fishing the surf about five years ago, and I absolutely love it. While there will occasionally be rivers and lakes near where you are travelling, the coast will be right there next to you the entire time. It is a free and endless resource.
A great book on the subject is Ken Hanley's "Fly Fishing Afoot in the Surf Zone"