Plenty of restaurants within walking distance to the Ritz.

I find this map is usually valuable for getting one's bearing regarding locations of restaurants.
http://www.caymangoodtaste.com/interactive_map.asp?mapID=13&Submit=Go

Not many higher end, truly Caymanian food places, but Alfresco's has a great setting. From the above websites search function on local food: http://www.caymangoodtaste.com/restauran...p;Submit=Filter