What gets me is how many times I walk past one of those airport exchanges and see nobody except the people behind the counter and wonder how the heck do they stay in biz. I reckon its a low volume, high profit biz.
I typically ask the hotel desk if they can exchange some US$ into J$ and give them a day or two to get it done. Most will hook ya up on their next bank run. You'll get a fair exchange rate. Easier than cabbing it into to town and hitting an atm.