Last time we were in Cozumel we went to Playa Corona (Corona Beach). Not much to it, a rustic little beach bar and you can rent snorkel equipment there. It was about $5 wach way in a taxi from the International pier, it would probably be about $10 from downtown. There was a $5 cover charge (for both of us). I'm not a huge fan of beach snorkeling but the snorkeling at Playa Corona was pretty good. There was some nice coral and schools of fish. The water was fairly shallow. Since we own our own snorkel gear and it was too early to start drinking we spent the whole morning at the beach for under $20. There are many other beaches in Cozumel to enjoy and lots of shopping downtown.
At Ocho Rios you could go over to the little shopping area. There's a Jimmy Buffet's Margaritaville there that has a private beach and a pool complete with water slide. Lots of beaches at Ocho Rios as well.
In Grand Cayman you could go to seven mile beach, a short cab ride form the tender docks. Lots of equipment rentals there. Everything from Sail Boats to Jet Skis, etc.
If you're only going to do one excursion on your trip, I'd encourage you to do Stingray City at Grand Cayman. You'll get in some good snorkeling and get to swim with the stingrays too. The most bang for your buck in my opinion.
Having said all that, although you're on a budget, do consider this. If there's something you've been dreaming about doing on your cruise vacation then just do it. Don't pass it up because you think it would be too expensive or for any other reason for that matter. I can't help but think how disappointing it would be to get back home and wish you had done something that you didn't do. My credo on a cruise vacation is "No woulda, coulda, shouldas". There a good reason that the following is posted at the top of the Cruise @ddicts home page...
Twenty years from now you will be more disappointed by the things that you didn't do than by the ones you did do. So throw off the bowlines. Sail away from the safe harbor. Catch the trade winds in your sails. Explore. Dream. Discover. -- Mark Twain
What ever you decide I hope you =funsign on your cruise.