I don't know if any restaurants in Playa actually offer Absinthe (the old Apassionado, now gone, used to have a bottle at the bar), but you can buy it in the liquor stores on 5th avenue. You will find the US approved fake stuff, a bright neon green Mexican Absinthe and the more expensive French and /or Czech wormwood based drink.
And don't let the party poopers try and disuade you. True worm wood based Absinthe does have a kick. Moreover as I have said before on this forum, what the naysayers don't realize is that there is flavor in the fact it is forbidden.
And while personally I prefer the power of Green Chatreuse if I want to dance with the devil, I think the tradition and ceremony (sugar, ice water, silver spoon, etc) of Absinthe is fun and worth the effort. Go for it.
Papa T