Here are my suggestions....
Long time lurker, but St John lover so I had to answer you.
First, what kind of beach experience are you looking for on St John? There are only a few beaches that have chairs and concession stands; Trunk, Honeymoon and Cinnamon. If you want a fantastic beach right on the road, but have to bring your own drinks and snacks then Maho is the one. Francis is my favorite place on Earth, but it's further out and no concessions at all. Remember, no glass bottles on beaches. I would also suggest renting a jeep for the day and driving around the island. Lameshur is a beach that you will never forget, but taxi's don't go there. You have to off road some, but it is so worth it. If you decide to rent a jeep for the day use Courtesy Car Rental. We've used them twice and will use them again in June.
If you've never been to Jost then you need to do some liver stretches. The most popular activity is drinking. Heavily. Are you going by ferry or private charter? The Soggy Dollar Beach Bar is fun and the Painkillers are great. Just remember that you have to swim back to the boat if you go by charter. White Bay is amazing and there are more bars to visit than just the SD.
If you want to do an awesome day sail on a sailboat to Jost then check out Kekoa at blacksailsvi.com. We had an all girl crew that started mixing drinks as soon as we finished snorkeling. We actually sailed across the channel instead of using the motors. They'll handle customs for you when you get to the BVI's. You'd have to meet them in Cruz Bay on St John in the morning of the sail.
If you've been to Jost before, please try going to Virgin Gorda and hit the Baths, Spring Bay and go eat at Hog Heaven. I would suggest renting a jeep from Mahogany on Virgin Gorda and drive around the island. We used them last year and it was easy. We did the credit card thing on the hood of the jeep, got a map and headed out. When we left on the ferry we just left the jeep at the dock with the keys under the mat. Virgin Gorda is a magical place and you should see it before the rest of the world ruins it.
I'm going back to lurking, but will check back to see if you have any questions. I will warn you, once you go to STJ, you'll only use STT as a means to get there!
Edit: I guess I replied to a reply in the thread. Whoops!