It depends on whether you can get out of Port of Spain or not. There are boats that target large tarpon in deeper water but there don't appear to be many flyfishing options - at least with info online. You can apparently hire a boat north of the city to target them in shallower waters. The Caroni Swamp south of the city (immediately west of the airport) is your best bet if limited on time but you'll need a guide/boat. I found "someone with a boat" by asking the driver that took me from the airport to the conference I attended (please note this can be a risky way of doing things in T&T). While I SAW plenty of tarpon none ate, but I did manage to pull one snook out of the mangroves.
You could try contacting the hotel concierge ahead of time to see if they can find someone to assist, or google one of the Caroni Swamp eco/bird santuary tour operators since they probably offer fishing as well.