In Progreso we caught a cab to Merida so didn't see a lot of the town. We did get a look at the beach & water there along the shore in Progreso. It isn't great. Better than, say, Galveston, but not nearly as good as Destin or Cozumel.
We did not book an excursion in Cozumel. We got off the boat and caught a taxi ($11) to Chankanaab park. Cost for the 4 of us was $70 to enter the park. This is a nice place. Be aware that there is not much actual beach. The only beach is along a small natural pool that connects to the sea by some small passages through the rocky coastline. This pool is about 3 - 4 ft deep, and had a lot of fish in it. We found a very nice flounder hiding in it. It is a great place for smaller kids to swim and snorkle. A caveat is to do this early as once more people show up the pool gets cloudy from people (sandy bottom) and one can't see anything. The sandy beach by this pool, while not large, was enough for us. If you want a large beach along the sea there are better choices in Cozumel (but w/o good snorkeling).
Along the rocky coastline there are several places with stairs to make it easier to enter the water. Around these it is fairly shallow and a good place for kids/weaker swimmers to see fish. Moving away from these stairs and going along the shore there are lots of fish. There's not a lot of living coral but there is some. Lots of sea fans. It does get deep quickly as one moves away from the shore. There is a floating platform anchored out there near some nice coral heads. I've snorkeled better places but this still rates well.
The standard dolphin encounters are quite $$$ (packages at $190, $150 and $100 pp is what we were first offered) but after we balked at the $$ the staff reluctantly pulled out an offering (not associated with Carnival) for a picture & limited dolphin interaction for a total of $70 for both kids. This ended up being a great deal. It lasted about 15 min total and my 2 kids had a dolphin to themselves. There was plenty of interaction, including a dorsal ride (with 2 dolphins) for my 7 yo son. The included pictures (one of each kid) came out great. We also saw the included (free) sea lion show at the park.
Chankanaab also has a swimming pool that is much nicer than the pools on Carnival Triumph. We only had 6.5 hrs ashore in Cozumel so we couldn't enjoy Chankanaab as much as we would have liked. It does make for a great day ashore.