I just came back from St John for two weeks.
The ferry ride is about 40 minutes. There is currently only one car ferry running so the whole ferry system is a little backed up. ( More people are taking the people ferry and avoiding the whole car ferry mess).
I don't think either of the big resorts allow guests to day pass. We own a villa at the Westin and the other biggie is Caneel Bay. (Which would be a little road trip to get to anyway)
Maybe Cinnamon Bay? It's a campground, so there are restrooms and a (not good) restaurant, but a place to get food.