re: Jamaica. Is it safe to leave the resort?

Just take the good advice of careful planning included in many replies already.

You know, it is a dang shame that perhaps the most beautiful(geographic) islands in the region also happens to be one of the less safe to visit.

Tip: Any location with a crap load of AIs is not ideal for traveling around alone unless you are well versed in the culture. A ton of people also do the DR every year because of price and it is a similar situation. They also typically find themselves encamped on a 40 acre resort for 7 days. The 40 minute shuttle ride from the airport to Punta Cana was all I needed to see. Poverty everywhere and armed guards sitting at intersections where shuttle buses passed through. Asked the driver what the deal was and he said they were there to deter locals from hopping on the bus and robbing everybody at gunpoint.