I have been to Cozumel twice.  Terrific diving reefs, great local
people (not so tourist-y), and you get a lot of vacation for your
money.  (If you're lucky, you'll be there for Mardi Gras.)

In terms of recommendations for dive operations:  We dove with a boat
by the name of Careyitos in Cozumel both times (my then-boyfriend, now
husband had been diving with them for 15+ years and recommended them).
We went for a total of 5 days (2 days diving, day off, 2 days diving)
(i.e., I had a good chance to see the operation).  The owner is Ricardo
and the divemaster is Tony.  They are absolutely wonderful -- I can't
say enough good things about them.  You don't want to get stuck on a
cattle boat.  The Careyitos takes around 10 divers and the price is
wonderful for what you get (around $75 per day, which includes two
dives, tanks (they can do Nitrox if you let them know in advance),
weights and belts, and a great lunch).  You get expert attention (they
take you to some really exotic places, through caves, and they will
point out and tell you a lot about local animals, flora and fauna,
etc.). If I remember correctly, you can stay down 75 minutes or until
you have 500 psi left per dive, whichever comes first.

They leave from a harbor around 10 minutes taxi ride south of the
center of the City.  You can find them through their website,
http://www.advanceddivers.com/  If you tell them your arrival time they
will tell you if their times work with your schedule.  (They leave
around 8:30 in the morning and get back around 3:30 in the afternoon.)
If you're interested and this fits into your schedule, write to Tony
and feel free to mention my name.  I highly recommend them over all the
other dive boats I saw in the area.

In more general terms, to answer your questions (at least with respect
to Cozumel), you can use American money, or you can use pesos (around
10 to the dollar).  I assume you will definitely need a passport to get
on and off the boat, but ask the cruise line.  Obviously, the most
important thing is to make sure you don't miss the boat back.  The
cruise boats dock right in the middle of town, and you can take a taxi
to the harbor where the Careyitos docks.  (It was around $5 American
each way, if I remember correctly.)

If the Careyitos doesn't fit into your schedule this time, you should
consider it for a subsequent trip.  We stayed at a little hotel in the
middle of town. Let me know and I can give you the name if you need it.
There are fancy hotels, but also lots of wonderful little ones, too,
and they're within 10 minutes walking distance from the middle of
Cozumel (the square).  And finally, Cozumel is extremely safe.

Have a great time on your cruise --
Cindi Beckwith

In GC you'll have several options. You can turn right when you reach the sidewalk and
walk about 100 yards to either of the first two dive shops and simply go shore
diving. You'll probably pay about $10 per tank, and a few bucks for weight. You could
potentially make 4 dives and spend less than $50. The diving there is fairly good,
but you'll probably be sharing your dives with a bunch of other divers from the
cruise ships (not that you may not find that with any diving you can manage while the
ship is there will be done with plenty of others). You can also head a bit further
down the road to Sunset House or Smith's Cove (a small public beach,but you'd have to
get your tank on the way). Especially with gear they're far enough that a taxi is in
order. The advantage of Smiths Cove is that there's a fair chance you'll be the only
one diving there. You can also take a taxi and head left to one of the shops in the
other direction, or get picked up by any number of shops.

That might be the plan, but there are no guarantees. If you go with the cruise's trip
they won't leave without you. If you go on your own and get back right after the last
launch heads to the boat you may get to buy an expensive airline ticket.

I just got back from a 10 day cruise to the Western Caribbean on RC.  We
dove Grand Cayman, Cozumel and Belize.  Like you, I had only dove Florida
before this cruise.

I recommend using the excursions arranged by the dive companies.  In all
three locations we had an excellent experience with the operators arranged
by the ship.  We used Red Sail in Grand Cayman, Sand Dollar in Cozumel and
Hugh Parkey in Belize, and were very happy with all three.  The operators
want to make sure the cruise lines are happy by following regulations,
safety guidelines, etc., and they want the cruise lines to get good feedback
from their customers in order to keep the business.  Also, if there are
delays in returning from an excursion you can be assured that the cruise
ship won't leave without you.  That's not true for "do it yourself"
excursions.  Lastly, everything is paid for ahead of time.  You may end up
spending a little more, but it's worth the piece of mind.

Oh, yeah, one more biggie for Belize:  Belize doesn't have a dock for big
cruise ships, so you have to normally suffer through long tender to shore
and back.  But on RC the excursion dive operator picked us up at the ship.

TT