Jost or Tortola...........what a sweet decision to have to make.
I must put a disclaimer out here that I AM A TAD BIT PARTIAL TO JOST!
Off Island day on Jost: (so many choices)
Ferry to Great Harbour, rent a vehicle or taxi to the East End, Jewel's (great rum punch and baked goods) and Foxy's Taboo (great boutique shop) at this end. A hike to the Bubbly Pool is always fun and a must do at least once in your life. Snorkeling around Diamond Cay is usually good for a turtle or two. Last time there, I saw my first spotted Ray. So cool!

If you can catch a ride in a boat then you can also hit B-line Bar while on the East End. Very laid back place to hang for the afternoon with minimal crowds.
Our Villa is on the East End of Jost so I love to hike the hills and spine of the island. If you are an avid hiker, you can go from one end to the other over the very high and beautiful spine of Jost. It is not for a beginner but the views are amazing. We are headed down in 10 days and plan on hiking from East to West with a reward of lunch at Hendo's, painkillers at Soggy, and then a taxi ride home. You can take this same hike in half (and/or from either end) and you will end up in Little or Great Harbour.
Off Island day on Tortola: (again, so many choices)
Ferry into the West End, taxi over to Soper's Hole and walk around and explore, shop. Grab a picnic lunch and head to Smugglers, Cane Garden Bay, or Brewers. Rent a vehicle and just drive around Tortola, so many cool old buildings and viewing spots. If you want to hike, check out Shark Reef Nation Park. Not easy to find, just past Brewers Bay, but a great hike and a beach that is very private. Walk around Road Town and explore some of the fun places to eat and shop.
The mood/atmosphere/vibe (not sure what the word I want to use is) in the BVI is different than that of the USVI. Take it all in, you are in paradise either way.