Just to add, there's a Holiday Inn Express not more than a mile away at the exit from 295. Nice enough with free breakfast and you have a 2 minute drive to the port. Very convenient.
As others have mentioned - accessibility in JAX is great! Parking is super close and painless. If parking at the port you can (at least we did in the past) pay online in advance and breeze right on through. Of all the ports I've cruised out of, JAX is my favorite.