I know Island Perk and Rehab (just outside Jaguars Temple) have two for one on local rum drinks. Most places will have their specials listed on the boards in front of their places.
And keep in mind that local rum drinks usually are half the price, or less, of anything imported. If a rum and tonic is, say, US$2.50 or $3, a gin and tonic is maybe US$5 or $6.
If you look at it that way, it's happy hour any time!
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