Falmouth has a nice shopping area right in port as well as Margaritaville resort. Maybe take some time to talk to the locals who are selling in the port and find out about their history and culture.
Grand Cayman: Shopping area close by as well as a wonderful old church right across the street from the port gates. It is amazing and beautiful. There is quite a bit of history there as well to explore.
You will have to tender, but it is a very organized and the tender boats are large and staffed by excellent and experienced crew and captains. They do this process so many times a day, week, month and year that they could probably complete the process with their eyes closed and a had tied behid their back.

Not that they would. lol
Cozumel: Again, shopping, rich history and culture to talk to the locals about. They have a Starbucks, a Hooters, and a Margaritaville here as well as some other cool places.
We have done this itinerary 5 times and sometimes we stay on the ship and others we just leave and wander. We have done the following excursions though and a couple of them are good for even wheelchair access.
Cozumel: Ruins and chocolate tour as well as a beach break. I think you would have trouble with wheelchair access though. If you can walk short distances and stairs don't bother you then it will work out.
Jamaica: Good Hope Estate tour, Green Grotto Caverns (NOT good if you are in a wheelchair or cannot climb stairs and hate enclosed caverns and bats) And High Tea at Good Hope. This was something we did a couple of weeks ago while my husband and son went ziplining. They have tea and assorted snack food (jerk chicken, cookies, finger sandwiches, etc)
Cayman Islands: We have done the Turtle Farm and tour of Hell (first time we went there in 2013) We have also just left the ship and walked around or just stayed on the ship.