Follow-up from our visit:
Calypso Grill was excellent. Bro-In-Law (a foodie) commented that he would be happy eating there every night for 2 weeks and would have a different entree every night.
We had an excellent lunch at Chicken Chicken.

Edited to Add:
We had an excellent, filling lunch at Vivine's near Gun Bay on the East End. Parking was limited. Lunch consisted of a main dish choice (I had BBQ'd chicken; others had spare ribs and fried fish) and included 4-5 vegetable/starch sides.
We also identified but did not get to try Tukka (also East End) and Over the Edge on the north side. A friendly person also eating at Vivine's concurred those would have been great choices.

We stayed at Renaissance condos on 7 Mile beach. Upscale facility, fairly centrally located. Comfortable, with great ocean views.

The last night we did a Biouminescence Bay tour. It departed from Cayman Islands Yacht Club, and included a very bumpy ride across the North Bay, which bothered one of our older members. Alternative was a long drive (probably 90 min) over to Rum Point. Several of our party got Jellyfish or similar stings while in the Bio Bay. The Bio Bay is a recent man-made body of water that the microorganisms showed up in a few years ago. What you see looking through a face mask in the bay appears to be small, glowing bubbles. The glow was not enough to be captured on GoPro video. I am not sure any of our party would do that tour again.