I don't know what I could be too much help. Given that you're focusing on stuff from Africa and the Caribbean, why not use some distinctive word or phrase from an African country or an island in the Caribbean?

But, maybe if you think you will be changing the food at some point or adding other foods, then you may not want to use something so specific.

Sticking to what you have, maybe something like Ethnic Food Fusion (and the domain name is available). Fusion of Ethic Foods; Food Harmony; maybe a tag line: The original home of African and Caribbean cuisine in Name of your City (because as you said, no one else serves such foods in your area).

Best of luck!

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