There are "no smoking" laws in Jamaica, island wide. The reason they were implemented was to create a safe, healthy workplace for the employees after universal health care was enacted. In air conditioned establishments and places with children, this was a common sense necessity. And in restaurants, not smoking is the polite thing to do.
While this is the law, based on a recent news article, only a handful of tickets have been issued. If caught, you are generally asked to put out the cigarette, and if you refuse the nice officer, you can expect a not so nice ticket... (grin)
In many open air establishments, as long as children are not around smoking is allowed.
If you call any hotel, please remember that small amounts of ganja are not legal, just decriminalized. Rather than an arrest and court date, you get a ticket and a fine, but no police record unless you dont pay the fine. Any hotel or restaurant would be foolish to suggest over the phone that you are allowed to smoke ganja in their establishment. There are still no legal ganja "coffee" houses in Jamaica yet, but that may be changing soon.
As for SATP, they have designated smoking areas, and smoking in their wooden rooms and wooden balconies is prohibited for obvious reasons.