Honeymoon beach is adjacent to Caneel Bay Resort.
There's a trail.
There no amenities on Honeymoon Beach to my knowledge. You don't need to purchase anything to
go there but if you park at Caneel and walk over they
do now charge for parking.

Can't tell you how busy it'll be but there's a company on STT that does daysails over there and has several boats that anchor just offshore, stern to the beach (they carry 6 persons each) and Ecotours does their trips to that beach.

If you're staying on STJ and have a car, there's lots of beaches that don't charge any admission. There's Hawksnest, Cinnamon Bay, Little Maho and Francis Bay, all on north shore, plus many more.

Truck Bay has a small charge for admission and a snorkel trail. If you pay to get in there, you have free admission to Annaberg Ruins on same day.
Gorgeous views overlooking the Narrows, the bay below, Water Lemon Cay, and Tortola.
Not to be missed.

National Park Service has maps for hiking trails and offer trips, excursions and activities.
https://www.nps.gov/viis/index.htm

Be sure to get the "things to do map." You can usually pick one up in front of the ticket booth at passenger ferry, by Starfish Market, National Park Service, various places at Mongoose Junction, Connections, also at airport when you arrive in STT and at the ferry on STT side.

If on STT and have a rental car, you can take the car barge from Red Hook over to explore. If you don't have a rental car, you can take the passenger ferry over to STJ and rent a car.
I'd suggest making a reservation, in advance if you go this route. Taxis make you wait until they fill up and then they drop everyone off wherever their going so you can spend a lot of time coming and going...and waiting around.

Enjoy your trip.