My son and I did the same thing when we were in Jamaica. We went right after breakfast. The cab driver was on time picking us up at Dunn River Falls, but there was a traffic jam in the parking lot that slowed things down a few minutes. However, he got us back to the shopping village near the Port with time to spare for shopping and browsing. We walked back to the ship and enjoyed a late lunch on the Lido deck.
I've also done the excursions booked through Carnival. I felt much better (timewise) with these excursions. The tour guides are adament about time spent to assure everyone getting back to the ship or shopping areas in ample time. Peace of mind is well worth the price.
The Cruise Director will always have an Island Talk a day or so before you reach your first port of call. They go over every excursion offered, complete with video. You'll be informed of what it consists of and what to expect. You're then given the opportunity to sign up for your choice(s) right then. Or you can sign up at the Pursor's Office. Even better, you can sign up in the comfort of your own room through Carnival's television station. Your tickets will be delivered to your cabin the day before your excursion.
I highly recommend doing it through Carnival.
Bon Voyage.
LadyDeb
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09/07/2001 - RCCL Majesty of the Seas
11/24/2002 - CCL Paradise
12/23/2006 - CCL Imagination
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07/18/2009 - CCL Destiny, coming up!