The Rosewood Apts in St. Vincent are inexpensive, and offer self catering accommodation with great views (and within walking distance) of Villa beach and Young Island, you might consider the Beachcombers Hotel which is right on the beach, they offer a variety of hotel rooms from budget through to luxury. The Young Island Resort might be a little pricy if you are on a budget.
Dive St. Vincent is located in Villa at the Young Island Dock. There are a variety of other accommodation options, most of which will require transportation to get you to a dive shop.
Indigo Dive is based on the leeward coast of St. Vincent, putting most of the leeward dive spots just a few minutes boat ride from the dive shop, but currently there are not any budget hotels or self catering apts within walking distance of the Buccament Bay Resort where the shop is located.
Dive sites that you should consider include:
Critter Corner (behind Young Island) - a muck divers macro heaven
Kingstown Wrecks
Kingstown Pier (no permits required, but if there is a cruise ship docked divers are not allowed)
The Bat Cave
Japanese Gardens (When there is a current this is a great drift dive)
Pretty Bay (Pristine soft coral forest)
Pinnicle
Tarpon Run
Anchor Reef
You'll find a number of videos to whet your appetite at
Kay Wilson - YouTube