caribbean bicycling opportunities?

Looking to spend 5-7 days on either Puerto Rico, Jamaica, Guadeloupe,
Aruba or Antigua. Would like to spend part of that time cycling,
either around the island or from a home base. I don't hear much about
cycling in this part of the world. Any suggestions/experiences? Open
to other islands, but not to a "all-downhill" or super touristy
experience. Prefer road to mountain biking. Would also appreciate any
ideas on bike rentals.