Wagons, or purpose built granny carts, complete with inflatable wheels, and hooks onto which you can hang your folding chairs are an option. Went with my toddler on Sunday. I took nothing more than a diaper bag, a queens sized flat sheet, and an umbrella. We stayed roughly 2.5 hours in the early a.m. (no beach traffic). Left the house at 8:30, beach at 9 am, stayed until 11:30, ate lunch in the car, and were tuckered out plenty for an afternoon nap.
If you aren't staying the whole day, you can easily leave a lot of stuff at the car. a change of clothes, baby powder, a few spare towels, aloe etc.
Also, on a side note, just be prepared that even if baby loves the bath, they might be afraid of the ocean. Sand and surf can be noisy and intimidating.
Good luck to you and yours,
F. B.