There are lots of great shore dives. Many of the ones on the west side have dive shops on site.
West side shore dives are lumped into two groups; West Bay and those south of Georgetown. Generally sites have healthier coral the further you get from the cruise ship terminals.
The group in West Bay includes DiveTech at the Cracked Conch (Turtle Farm), DiveTech at Cobalt Coast, and Spanish Bay Reef Resort. The wall is a steep drop as is typical of North Wall sites.
The group south of Georgetown includes Eden Rock, Abanks Dive Centre, Don Foster's Casuarina Point, Seaview, and Sunset House. Sunset House has a small wreck and the famous statue of the mermaid Amphirtite. The wall is more of a sharp slope rather than a sudden drop throughout this area.
Though logistics are more difficult, other shore dives around the island can be much better than the west side sites. You'll need to rent tanks and weight elsewhere for these. Be forewarned that you should call ahead to the East End shops if you are planning to stop and rent gear - not all of them rent tanks or other gear for shore diving!
Beach Bay is on the south shore between Savannah and Bodden Town at the end of Beach Bay Rd. Be wary of sea conditions!
On the north shore along the Queen's Highway is the famous Babylon. Directions you will find on the net are for entry through property that has been closed to the public. You'll have to drive further west (and swim further) for an accesible entry. Swim towards the mooring balls which sit on the edge of the main wall.
About 200 yards east of Barefoot Beach Gardens on Queen's Highway is a public access point down to the beach. You'll have to kit up and hike west a couple hundred yards to get out past the inner reef. The wall in the area sports some of the huge barrel sponges that make the dive truly worthwhile.