Davin Ebanks is the best on Grand Cayman. He will get you on to large tailing bonefish on foot. There are some tarpon in canals and under some of the lights, but that's an evening adventure. An afternoon or two with him and you can get out on the tides on your own, but you'll benefit from his eyes. You fish mostly turtle grass for the bones so blind or lightly weighted flies with weedguards are the order of the day. The fish are tough but genuinely large.
You can see bones up by Cayman Kai and Rum Pt on white sand, and some huge "pet" snook under the Rum Pt dock. The good flats are along the south side, though.
Understand Little Cayman has a bit more to offer but haven't tried it.