Trying to do an inexpensive trip on the most expensive island in the Caribbean? We did it 2 yrs. ago. Some options:
Lunch at My Bar at Sunset House. Great sandwiches under $10 US. Plus you can dive there. Get your picture taken with the Mermaid in 50fsw. Also check out the Cathy Church U/W Gallery/School in the basement of the main house. It's about a $10-15 cab ride from the middle of SMB.
There's a sandwich shop in the first strip mall on the ocean side of the main road just south of Treasure Island. Nothing over about $6-8 US. Really good food. While there check out the divestore in the same plaza, it may be the best one I've ever been to.
We also had a good meal at Athena in front of Treasure Island, but it was pricier.
There's a KFC just past the turn towards SMB coming from the Airport. Also there's A Burger King in Georgetown. And a Hard Rock Cafe - fairly reasonable with a great view.
Other diving: Turtle Reef on the North End, you can rent scooters for about $40 to get out to the wall, or just swim along the mini-wall 40yds. offshore. I've read it's the better of the two Divetech locations for shorediving since the wall by Cobalt Coast is farther out. A long ride by cab from SMB though, it's in a pretty remote residential neighborhood, the only thing nearby is the Cracked Conch restaurant upstairs.
You should definitely do the Stingray City dive. It's really a memorable experience.
We dove Eden Rock in north Georgetown, it's a nice facility but the dive is pretty marginal. Too many tourists over the years since they're the closest divesite to the cruise ship port. And it ends in about 40' unless you want to swim under the Jetskis/Cruise Ships(can't - just kidding) farther out in the harbor.
We rented a car to go up to Turtle Reef, I think from Andy's. They'll pick you up on SMB. If your place has a kitchen and you're planning to do some cooking, the main Market(Hurleys?) is just 2 mins. from the airport, so you might want to stop there on your way to SMB. Prices are really high since everything is imported.
We did the whole trip with a 2BR condo on SMB, not including airfare for about $1500pp. Including food and 4 days of boatdiving.
Diving is the main attraction on Cayman. There's also the Turtle Farm, now called Boatswains Bay or something like that. They advertise in PADI Sport Diver. Also there was supposed to be a waterpark with a wave machine being built near there, not sure what happened to it post-Ivan.
