Most of the shore dives in their van are likely someone else's property with on-site tanks so if 7Mile Diving is charging for that it's easy to DIY. The way it works on Cayman is the on-site resorts own to the waterline and most won't allow outside tanks to be transported across their property. They can't deny you access to the ocean but you get the idea. I don't exactly remember what we paid but it was reasonable.
In the NW Point/West Bay area there's 3 good options. Turtle Reef, Lighthouse Point and Cobalt Coast. Sundivers is at the first one, Divetech the other two for tanks etc. I like Turtle Reef, I'll dive it everytime I'm there. It would work for your newer diver also, there's easy stairs, a small cove to get oriented, then a short swim (40-50 yds.) out to the Mini-Wall. To the south is the Tarpon Cave - they're always there. Across the sand flats a considerable distance it's also possible to access the North Wall - more advanced diving. At one time Cobalt Coast offered tows out the the North Wall from their farther east location also so you could swim in. Never been to Lighthouse Pt. to dive.
Turtle Reef | Scuba Diving in West Bay | iDive Cayman
Shorediving - Cracked Conch Grand Cayman Ocean Front Seafood Restaurant and Tiki Bar
Grand Cayman scuba diving - Divetech
IMO most of the Georgetown area sites are a little tired - a lot of cruise traffic since they're walking distance from the port. Those include Eden Rock/Devils Grotto, Cheeseburger and Foster's reef - all are along the waterfront downtown. So is the cruise tender port - it's 500' from Eden Rock - IMO the worst dive we did all week. But shallow.
Although the Grotto can be excellent when the Silversides are in during early summer.
Silversides in Devil's Grotto, Grand Cayman, June 2013 (colour) on Vimeo - the rest of the year it's you and the few tarpon that are left hoping...
Slightly farther south of town is Sunset House -
Sunset House - George Town - Cayman Islands It's pretty optimized for shorediving - even has a Saltwater Pool that's open to the ocean on one side - your new diver could easily manage there. My Bar there is the divers bar.
A short drive past it is Smith's Cove - kind of a shallower site. No facilities so rent tanks at Eden Rock or Diver's Supply in town for it.