I know that some of the diving in Cozumel can be beyond a new diver, but
a decent instructor would not do open water check out dives where the
currents were strong.  Which brings up the usual point about the
instructor being very important.  The diving in the Keys won't be as
good as the places you mention, but you can drive to them (if cost is
important).  The dives and the instructor might be a little more
expensive in the Keys, but the cost of transportation and the days spent
can be less.

Perhaps, or perhaps not:  one could just as easily go your checkout
dives in a local mudhole or quarry, whith the understanding that they
can look forward to virtually "any" tropical warmwater as being
better.

If the suggestion is the FL Keys because they can be driven to, then
what should also be considered are some of the FL Freshwater
Springs ...that often offer better viz... and save 5-6 hours each way
off of said drive.

And if the instructor's coming along in the van on this road trip, you
could actually plan for the Springs to be an overnight rest stop where
you spend the afternoon doing the first set of checkouts, then the
next morning doing the rest, then you hit the road in the afternoon to
drive the rest of the way to the Keys with those dives out of the way.

-hh