Luz's Restaurant in Cayman is a very popular local restaurant run by the establishment's namesake, Luz. They serve authentic local Caymanian and Honduranian dishes. Their fried crab, turtle and Cayman style lobster are all particular local favourites (especially of the Good Taste Editors!). The local menu is set weekly so be sure to call and ask what they have on any given day.
The restaurant itself is well maintained in a nice neighbourhood near the schools and the hospital. They have ample parking.