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Have you ever heard of finger limes? Think of pop rocks but citrus. When you open the finger sized pods, they are filled with yellow, pink or green spheres. Put these in your mouth and they explode with a lime like flavour. So as well as the flavour there's also a "fun" component to them.
Finger limes are Australian natives, but are now being grown in California and, I think, in Florida. But they're not common yet so would be kind of a fun thing to have on a menu.
Morel mushrooms! These grow only near dead oak trees and are wonderful. You slice them lengthwise, dredge them in flour and fry them in butter or olive oil. They aren't cultivated and so are very rare. I don't think these would grow in Florida, but up here in Zones 3 to 5, they grow well, if you can find them. (They are very hard to find and those that do find them, keep the location a secret.) I have seen them only rarely for sale in a super or farmer's market.
Two months ago I couldn't even spell freelance writer
and now I are one.
I garden in Zone 7, but I suppose what I'll suggest could be grown in Zone 9. A couple of people already mentioned heirloom tomatoes. Those can be tricky to grow, but the variety and taste can be worth the trouble--might be something customers at your cafe would keep coming back for. You might also want to consider fruits and vegetables in colors that are different from what we typically think of--black peppers, tomatoes that are orange on the bottom/purple on top, purple carrots. I'm not making these things up! In fact, the seed catalog I order from has all these, and they're all organic and non-genetically modified. Maybe you'd want to have heirloom tomatoes that are an unusual color. You might also want to consider melons--huge variety there (orange-fleshed watermelon, maybe). I'm picturing a cafe that has it's own garden, so the owners/employees can grow their unusual item from seed/don't have to depend one someone else for it.
In Zone 9 you should be able to grow loquats, a kind of fruit with orange flesh and large seed/pits which is common in parts of China.
Celery is hard to grow but easy to buy, so probably doesn't fit the bill.
Artichokes would be a good choice because there are some interesting varieties and they're very attractive plants (I think). In Zone 9 they would be perennial and could maybe even stand in for ornamental bushes.