Hi, Rich!
Well, to tell the truth, Coz is a diver's town except for the shopping, which I avoid like Monteczuma's Revenge. At any rate, for non-divers (poor souls) there are two things to do:
(1) They can take in the shopping like the cruise ship folks. It is very easy to do since the mail street Av. R. Melgar is lined with shops, as is the El Centro, the plaza. One shop that used to be worth seeing was Roberto's, the Black Coral artist. If you want to buy a black coral carving, go there (Av. 5. Sur 199). He is open from 9 AM-2 PM, 4 PM-9 PM on weekdays only! Back in the good old days, before the cruise ships and before he got a little long of tooth, his shop was like an underwater art museum. However, there are still lots of good things to see there and you can order something from him if it is not on display--ask to see photos: he can be trusted completely to send what you order. One warning, though, he is pricey and, so, if you are just looking for a trinket, go to one of the shops on Av. Melgar. I have several of his pieces and they are glorious. If you are lucky, he will have an octopus and/or a splendid toadfish in the shop (or a hammerhead or manta ray).
Sorry for the digression.
(2) They can rent one of those sporty, topless VW's and circumnavigate the island. On such a tour, the most common route is the southern one taking one to the Mayan ruins at El Cedral (left turn just after the beach at Playa del Sol) , by a bunch of beaches that some like, but I think are non-descript, the light house at Punta Celerain, the nice beach and bar at Mescalito ("The Last Frontier"), and points north. Mescalito is a good place to stop for a beer or whatever bebida is on your mind and walk down to the beach. Awhile back there was a nude beach there, so if some folks in your group are sensative, don't wander too far.
Heading back north, you come to Av. Benito Juarez and make the left (west) turn until you come to the sign for San Gervasio. These, too, are Mayan ruins that are worth an hour or so. There is a decent gift shop there, too, but not many things different that what you can find in town. Chacmol was the bloody god whose stone statues served as "operating tables" for the human sacrifices of the Mayan. You can find small versions of him in various media (terra cotta, onyx, etc.) at the shops there.
Note: the more adventurous folks take a less traveled and somewhat more challenging course--which I do not recommend, in general, but mention here for the sake of completeness--the way north. You head to the Punta Molas light house and the ruins at Castillo Real. This is the "jungle" part of Coz and you can see lots of iguanas, large snakes (mainly boas) and, believe it or not, crocs! (Oh, yes, mosquitos and scorpions, too!) But the road is very rough, not well-travelled, and not to be taken lightly (4-wheel drive for Norteamericanos, but locals do it in those VW's!).
Okay, now to bars and restaurants. I am not much on bars and you did not mention the ages of your group, so I will just make a few general suggestions. As for bars, I guess the most famous is Carlos 'n' Charlie's, recently moved to the new pier area. Geez, but it is noisey and filled with the younger, drunker set! But that might be your group's preference. Las Palmeras has signs all over the place and lots of folks like to sit at their outdoor tables (under a shady roof), drink and people watch; it is right on the waterfront not far from the central plaza. My opinion: stick to the cerveza (beer) and drinks--the food is only so, so.
Now, as for food, there is a another thread in this section about all the favorite restaurants on Coz. Have a look at it. My favorites: Guidos at the far north of town and the French Quarter--just down the block from Roberto's Black Coral shop. Lots of folks like Prima and it has a nice upstairs area that is most pleasant for lunch. Another nice place that we have enjoyed is La Parilla (it means, "grill" in Spanish) for some good Mexican food.
Well, I am certain that I have offended someone with my recommendations, but such is life! Enjoy the diving on Coz--maybe your pals will see the light someday, too!
Scorpionfish