"My problem with the Palms (and other places, for example Push Cart) is that they charge U.S.$ for the drinks at the bar."
That's the case in most places on the beach and more and more places on the cliffs. I don't ever remember seeing that 10-15 years ago. As a matter of fact I remember some years back the US/JMD exchange rate changed so rapidly in a period of three months (went from something like 65-1 to 80-1 between November and February!) that they were busy changing prices on everything at HiLo. That's when it dawned on me - so many people out there DO NOT change their money to local currency and then suggest other do not either like its a big deal.
The result - higher prices, US priced menus....I too try to avoid places like that. Of the five or six beach places where I looked at menus for drinks and food only one (Wild Parrot) posted their prices in JMD.
On the cliffs you are more apt to see prices posted in JMD but there are places such as PushCart, Rockhouse, Ivans and LTU that price in US. At LTU where I'm known I always get my bill in JMD. At Ivans, after doing some quick math in my head, I found their exchange was fair. Haven't eaten/drank at Rockhouse in years - and was only at Pushcart once for their Grand Opening.