St Vincent is not really a shore diving destination. There is no dive resort with shore diving. Or dive resort at all, really. If you look at shorediving.com all of 2 sites are listed. (I think I have dove one of them, New Guinea Reef, by boat.) We may have dove a few other sites by boat that were off public beaches, so there may be more shore diving possible, and simply undiscovered because there's not a huge number of divers going there, never mind ones trying to find it. But it would be an exploratory mission with a lot of driving and little advance knowledge of what's out there, currents, etc. Even the leeward side where you would dive gets pretty windy sometimes and I've been on some exciting boat rides along there. You'd probably have to start by finding any dive site maps from one of the dive ops and compare it to a local map for proximity of roads and beaches. Not something I would try, personally.
There's only a few dive shops and I'm not sure any support shore diving. We have always stayed at Young Island and dove with Dive St Vincent. We have done 1-2 shore dives from the beach there, Dive St Vincent delivered tanks to the island for us. Likely not an option if you're not staying there. It was ok just to see what was there but not something you'd necessarily repeat, and shallow near the island so you can probably see most of it snorkeling. (Deeper in the harbor/channel between there and the mainland, but mostly sand.) We also did a night dive by the island once, by boat for support and concern about what currents might be like if you approached the channel on the other side of the island. Interesting, especially the hundreds of flying gurnards scooting around the bottom, but again not something you would necessarily repeat.
There are a few small hotels on the mainland side of the channel and a couple bars & restaurants. And maybe some other places to stay scattered around. There's a larger resort further up the west coast that used to have a dive op, don't recall about shore diving, but last I heard it was bankrupt so not sure that's still open. For better or worse it's not an island with a big tourist or dive infrastructure.
We like St Vincent diving. It does have good muck/macro, and the occasional other surprise. Lots of seahorses & frogfish. I think bigger stuff tends to be fished out. Diving gets better the further north you head along the leeward coast, where the dive ops don't get much. We especially like the diving because we can do it while staying at a cool little resort. But getting there is a pain. They've finally opened the new airport that can handle more than puddle jumpers but air service has not improved much yet. You might be able to get there on Caribbean Airways on a slightly larger plane now from another island (maybe Trinidad?) There might be some flights from Canada, possibly charter. Maybe seasonal. Also maybe expensive. But as far as minimizing stops, you're not going to have much choice.