The weather in June is settled with lighter winds and waves.

Day 1 - I usually anchor in the bight, but the water is 50-50 feet deep and most likely your charter boat will not have sufficient chain for that depth. While there are shallower spots, they are hard to find and don't have great holding. I'd plan on a mooring ball in the Bight.
Day 2 - I'd go to Leverick Bay. You can anchor in good holding in 15-20 feet just outside of the mooring field. Or if you prefer to stay aboard, anchor off Prickly Pear close the the Sand Box.
Day 3 - Enjoy Anegada!
Day 4 - Rather than the north side of Tortola or Guana Island, sail to Jost and spend a night off Little Jost. The anchorage is quite protected. Ashore you've got my favorite beach bar (the B' Line) and for dinner there's the option of Foxy's Taboo. If you are early enough, you can walk to the bubbly Pool.
Day 5 - Sail across to Cane Garden Bay and stop at Sandy Cay / Sandy Spit on the way for a beach day.
Day 6 - Great Harbour on Jost and enjoy those painkillers!
Day 7 - That last night is always a tough choice - you could do Peter Island as planned, or repeat the Bight or even spend a night at Cooper Island. All are within easy reach of Road Town for a morning return.