I've dove Coki Beach before on a trip to St Thomas. There isn't anything wrong with it, but the boat trips are much better and worth a few extra bucks. Coki Beach just wasn't all that exciting compared to the better coral on the boat dives. Coki beach is the "beach destination" place for a lot of the cruise boat lines we found out after we went there. it was packed with people on the cruise boats doing a beach excursion, snorkle excursion, etc. We did notice a few other people there shore diving as part of a cruise trip.
though we dove with a different boat/shop, I've heard good things about Chris Sawyers operation. I've been in his shop. He's located down in Red Hook which has some very nice dive spots near it. I think a taxi ride from that area to town(port) was about $12-$15. They might offer a pick up service though if you book enough divers.
On Nassau, if timing for Stuart Coves doesn't work out, there is another dive shop over the bridge towards Atlants that is much closer to the cruise boat dock. (you can see Atlanta from the cruise boat dock and it's a few bucks ($5 to $8) for a land taxi or water taxi over. (I suggest the land taxi if you're hauling gear).