I really doubt that you will find one excursion that will please the whole family with the spread of ages that you have. Your teens probably will want to go on more active excursions, whereas your parents probably will wnat to take in the sights. Sometimes it's best to go in different directions during the day and then to compare notes over dinner. The good news, though, is that many Caribbean ports offer 1/2 day excursions that are very affordable.
Grand Cayman has several significant attractions, but I highly recommend a tour since this is a tender port.
>> Stingray City is always popular with the younger set.
>> Seven Mile Beach (which really is only 5 1/2 miles long) is one of the best white sand beaches that you will find anywhere.
>> The world's only sea turtle farm actually does raise the creatures for food, and also works on preservation of endangered species.
>> The infamous rock formation at Hell (which looks volcanic, but really is limestone that algae have darkened and eroded to razor sharpness) is an interesting stop on several tours.
>> The free port of George Town, right across the street from the tender pier, offers some of the best shopping in the Caribbean.
The excursion called the "Sea and See" tour is one that your whole family might enjoy. This 1/2 day excursion combines a cruise in a "semisubmersible craft" with a land tour to the island's major attractions. The "semisubmersible craft" is a special boat with a compartment below the waterline where you sit, two by two, and look out through windows in both sides of the hull. The cruise visits two wrecks -- those of the SS Callie and the SS Balboa -- on reefs near George Town. You'll also see lots of tropical marine life in its natural habitat. The land tour includes a narrated drive through George Town, a photo stop at Seven Mile Beach, and visits to the rock formation at Hell and the sea turtle farm -- in short, the island highlights. The walking is pretty minimal and there's a lot to hold the interest of your teens -- who might really want to take the excursion to Stingray City....
The island of Cozumel is noted for its beaches and snorkeling opportunities, and it has two other significant attractions. There's a very good cultural/folkloric show right in downtown San Miguel de Cozumel, and there are some Mayan ruins on the island at San Gervasio. These ruins are not as extensive as those at Tulum or some of the other sites, but they are much more significant because the island of Cozumel is sacred in the Mayan religion. The 1/2 day excursion that combines both of these attractions probably would be suitable for your whole family, though again your teens might prefer to go swimming or snorkeling.
If you are up for a more ambitious tour, consider the excursion to Tulum -- which is a full day adventure. The excursion takes a ferry across the channel from San Miguel de Cozumel to Playa del Carmen (on the Yucatan Peninsula), where it transfers to a bus for the ride to Cozumel via a new divided highway that's in very good condition. At Tulum, the guide will explain everything and then give you some time to explore the ruins in depth on your own. There's also a visitors' center that sells souvenirs and, if I remember correctly, snacks also. When the group boards the bus for the return trip, the guide will distribute boxed lunches to eat on the way back to Playa del Carmen, where the group will transfer to the afternoon ferry back to San Miguel de Cozumel. It's a long day and it's not cheap, but this tour is an excellent educational opportunity for your teens.
If you decide to go to Tulum, be sure to bring a liter (large bottle) of water for each person in your party from the ship and to drink from it frequently to prevent dehydration, especially while you are in the archeological site. The temperatures there tend to be in the 90's at that time of year, so dehydration is a significant consideration.
There's also an archeo-ecologial park at Ex Caret, also on the mainland, to which I have not been. I gather that there are areas for swimming and snorkeling as well as excavated Mayan ruins, but I really don't know the details. The drill is similar to the tour to Tulum, though -- ferry to Playa del Carmen, then bus to the site, and the reverse to return to the ship. This tour might well offer something for your whole family.
If you decide to do anything on the mainland, I highly recommend taking an excursion from the ship rather than going on your own -- if only because the ship will wait for an excursion that returns late, but not for a passenger who is not on an excursion.
This is a new port of call. I have not been there, and consequently cannot adivse you.
Have a great cruise!