I think you'll find that it's almost impossible to find a resort on Cayman without a pool. One of the least expensive places we found was Sunset House. I think they even offer some sort of AI package, at least they bundle the room and the diving. I have heard that since they are south of Georgetown that they dive the southern sites more if possible rather than running up to the North Wall. Not that that's a bad thing.
Post-Ivan they've refurbished a lot of the rooms so it should be pretty nice. Although you aren't looking for them, there is a pool, restaurant and also My Bar, a sandwich place that's a local divers hangout. It's 2min. to Georgetown, the market etc. also. Not sure if their rooms have kitchens though. And there's good shorediving right offshore.
Divetech/Cobalt Coast would be another good option. It's also some sort of modified AI. The downside it has (for me) is that it's pretty far north of SMB and the stores etc. Not a problem if you buy their meal plan, otherwise it will be a 10-15 min. drive minimum to Georgetown. It's the closest resort to the North Wall also, but it's a healthy swim from there. They'll drop you off by boat or rent you a scooter if asked.
Grand Cayman is still the most expensive Caribbean destination we've ever gone to if that's a factor in your decision.