“You would probably do as well to just stop at the public beach in New Smyrna which you would pass on the way to the Nat Seashore.”
New Smyrna Beach is unique because you can drive on the beach, its so much nicer than going to Daytona. Its $20 to get on the beach, or park... so there is that to remember. Flagler Ave is a neat little surf town-like area in New Smyrna Beach.
I’ll second the New Smyrna beach. My brother took me there, and later to Daytona. Much more “real” on NS. Daytona was full of South Americans.