In Grand Cayman we just wandered the town. There are a lot of shops. Then we took a cab to seven mile beach, rented a chairs, swam and walked where no one was.
It cost us about 30.00 for the day.
In Cozumel we rented a jeep, about 40.00 and toured the island ourselves. Found some neat beaches.
Tours are not always the way to go. Make your own memories. Be adventurous.
Both Grand Cayman and Cozumel are tourist friendly. Have fun.