This is what I would consider: fly into Beef, catch the next Speedy's to VG, rent a car, stay a week at GSB, do a day trip from Gun Creek to Saba and a couple of day trips by boat, including Anegada.

Then ferry back to Tortola and spend the rest of your honeymoon at Sugar Mill. Visit the spots recommended up thread. Easy taxi to the airport for the trip home.

IMO, that's the best balance of relaxation, sight-seeing and budget.