We just came back from Triumph cruise out of New Orleans on 2/6. Carnival advised for Progreso to take a tour off the ship. I can also vouch for this as we have been to Progreso 3 times. It is kind of scary to walk around in their downtown area. The flea market especially. This trip we just got off and went to the shopping area right there at the terminal area. We have done the Corona Beach Break - waste of money as drinks are watered down and the beers are about 10 oz. Our daughter and her friends that went did the Resort Deluxe Beach Break and really liked it. Good service, Good food, Good Drinks.
In Cozumel, we docked at Puerto Maya which has a very nice shopping area with a lot of the same shops that are downtown - be advised a lot of the shops in the port area will bargain. Taxi from this area to downtown is $7 and that was for 2 of us. There are guys on little bike type taxi (for lack of better word) that will take you to end of pier - and to taxi stand - for tips only. If you use them, they will usually watch for you when you come back and will ask if you want ride back to ship.