I can recommend Chris Sawyer out of Red Hook. They do a nice job.
Chris Sawyer moved over to St. John last year:
Welcome to Chris Sawyer Diving Center at Caneel Bay Resort, St.John, USVI
I've read someone else took over the diveop in Red Hook but have no details.
OO, an alternative would be to do a Rhone dive out of Tortola. Certain days it's possible to leave either Charlotte Amalie or Red Hook on a commercial ferry and be there later that morning. The Tortola to Rhone run is much shorter, probably under an hour. You'll want to do 2 dives as the front and back are separated by enough distance that most diveops move moorings during your SI. I would
guess that you could be back on Tortola around 4PM or so. On Wed. there's a last ferry leaving Tortola at 5:30 PM so s/b plenty of time to get back. Or go over to St. John in the morning first and then onto West End Tortola. It's often dove as a cruise ship dive from Tortola so they must have it worked out to be back early enough.
But a couple of things to know: Tortola is a really long island and the two stops - West End and Road Town are miles apart. So make sure both diveop (pickup?) and ferry stop are the same. Otherwise it's a cab ride across to Road Town - and the time it takes. One of the diveops there is at a resort on the East End so slightly further away. AquaVentures or UBS in Road Town do the Rhone, not sure when.
Here's the BVIScuba page, it lists most of the diveops on Tortola with links to their sites. I can completely recommend DiveBVI if you can get to Virgin Gorda and back in time, but I doubt you will be able to.
http://www.bviscuba.org/portal/DiveShops/tabid/58/Default.aspx
Some of the ferries are fast - doing the crossing in as little as an hour - esp. Cruz Bay to West End as it's the closer part of both islands. It's how everybody gets around. My friends left Virgin Gorda one morning around 8AM and were back in Charlotte Amalie early enough that they shopped for a
couple hours before their 1:30 flight.
You also have to clear customs/immigration both ways so bring your passport. I don't know what it's like on Tortola, but Virgin Gorda was quick. As was coming back into St. John. I think there's even some night ferries from St. John back to Red Hook, it's 20mins. or so apart.
Here's the ferries schedules:
http://www.vinow.com/general_usvi/interisland_ferry/ I don't know if it's still the case but a couple years ago I was told to call first to make sure they were running when we were there, some are seasonal.