If you want to keep things cheap, then stick to shore diving. There's great shore diving at sunset house, eden's rock/devil's grotto, and some other sites which are both really close to georgetown. Venturing farther way, turtle reef (the divetech site at the cracked conch) is fantastic. I'm sure there are tons more around the island too.
If you want to do boat packages, then you are going to pay a lot more money. From the research I did a while back, all the operators were around the same price point for dive packages. But if you want to maximize your diving value for a 4 day trip there, i think you probably can keep plenty busy with some of the fantastic shore diving sites that grand cayman has to offer.