if the OP was american and had US dollars to begin with I'd say that's the way to go... but when you are given a rate in US dollars understand that it has been set and quoted considering an exchange rate (including the exchange premium that is always charged) because Jamaicans do their business (outside of the resort areas) in Jamaican dollars (try going into a grocery store, a car lot or even burger king, ect)... (remember it's unlikely they are shopping in the craft markets or eating at the more expensive restuarants that are quoting in US dollars, they quote these prices for the tourists because that's their primary (and often only) customer....
when you are not coming from the US, IMO it makes pretty much zero sense to exchange your cash to american becuase it's essentially a dual exchange.. US dollars are widely accepted and are good for tipping (that's about the only reason I might suggest to exchange, b/c its easier for most people to think to leave 2 US dollars than something like 142J)...
i always collect US cash here or there whenever I come across it (which living close to the US, is frequently), but I wouldn't purposely exchange my money (outside of maybe 20 to get me to the bank machine once I land if I don't have any Jamaican kicking around, Jamaican cash is a bit harder to get outside of Jamaica, typically have to order it and I am usually not that organized...)
if you have to exchange your cash, there's no question... exchange directly to Jamaican... bring a currency cheat sheet (I don't have a link handy, do a google search)...
when you ask for a price in Jamaican that has been quoted in US, they likely will give you a proper one because they think you know the runnings, but it's best to find out... there are opportunistic people everywhere, they hear the accent and may decide to take some advantage
remember since the smallest bill is a 50 and no one really likes dealing with coin all that much, they may round up or down to the nearest 50... you can always make a fuss over this but honestly is 20-30J (which equeates to maybe 5 pence? my conversion to pounds is poor) worth arguing over? It's my understanding that the conversion from sterling to Jamaican gets you some advantage over the US dollar, so it's give a little take a little...
all and all, Jamaican dollars will typically go further if you have a little understanding of exchange rates and whatnot... you will also, as I said, help the local economy and be paying them in a currency they can use anywhere without hassle (in Kingston you won't or hear US dollars quoted anywhere)...
in Jamaica money is money and they will rarely turn it away unless it is obviously fake (I've seen people using yen for craps sake), but it's in everyone's benefit if you use Jamaican..
i also agree with using bank cards in local machines... I'm almost sure Barkley's banks have an alliance with Scotiabank (I've used my Scotiacard in both Scotia Machines and Barkley's machines without service charges and gotten good exchange rates on trips to Jamaican and the UK, so it seems logical that you could use a Barkley's card (if you are a customer) in a Scotia machine in JA and experience the same (but I will double check and post back if that is not the case)... it saves so much time (machines are widely available) and allows you to only have the cash you need on hand.... as mentioned there is a Scotia machine right down the road from RDCC (I've used this one a few times, it's at the end of the plaza with the L&M Grocers (pretty sure that's what it's called), coastal side of the main highway...
whatever bank you bank with, ask if they have an alliance bank in Jamaica and if they waive service charges when using their machines... (if not, then expect 2-3 pound service charges per transaction)
Chelle