There was no information provided on the ship for Cozumel unless you took an organised trip. The town is a taxi ride away and there are only a few bars and the usual cruise port facilities within easy walking distance. There are a couple of bars along the water front with diving facilities and quite nice places to sit and enjoy a margarita. Beware of the prices though. The drinks on the ship were less expensive and better quality!
Xunantunich is quite a trek from the port, a two hour coach ride, but well worth the effort. To fully appreciate it you will definitely need to be relatively fit so you can climb up to the top of the ruins or at least make it to the base which itself requires a fairly energetic uphill walk. The guides were excellent and displayed great knowledge and enthusiasm for their cultural heritage. The stop for food was brief, not wanting to take away time from enjoying the main attraction. The food was an appetising and interesting dish of rice and beans with seasoned chicken and fried plantain. No drinks were provided so expect to spend $2 on a local beer which is well worth it, and 1$ on an excellent local ice cream. This trip will consume the entire day so you won't get much opportunity to buy souvenirs but it is well worth the effort.
The port at Mahogany Bay is very nicely appointed. There are the mandatory Dufry's duty free, Diamonds International and Tanzanite stores amongst others. Then there is a bar run by Fat Tuesdays'. A very expensive chair lift ($12 per person for a one day pass) will take you to the beach area. It's only a short walk which is quite pleasant and there is a nature trail route alternative which is also very pleasant to stroll through. A lot of effort is being put in to keeping this place in tip top condition and it shows. The beach is very well stocked with free loungers. You can hire shades and floats if you like or just sit on a lounger with your ship supplied towel and do your own thing in the crystal clear water. A roped off area of water keeps people from straying to far out but there is plenty of room for everyone. More Fat Tuesday run bars and food are available at the beach and prices and quality were competitive. Look at this experience as being similar to the private Bahamas Islands beach stops popular with the Royal Caribbean crowd. To see anything else in Roatan you will need to take a taxi or an organised trip.
The port of Georgetown is packed with the obligatory jewellery and souvenir stores with all the familiar and monotonous Diamonds International, Tanzanite etc. facilities represented. There are a few local bars but beware of expensive prices. Breezes on the Bay looks like an interesting stop sitting on the second story of the main shops overlooking the port. At first glance the prices look a little steep at 8.95 for a Hurricane, but when you add the automatic 18% gratuity and then factor in the Gran Cayman dollar to US dollar exchange rate (prices quoted are NOT US) you are projected into the stratosphere spending almost $26 US for two Hurricanes that were average at best. Better to go back tot he ship and have a couple for $16 which you will enjoy more for price and taste. Grand Cayman is know for its sea activities and water is definitely incredibly clear and teeming with life. I would recommend taking a trip to experience this location at its best.