You can obviously buy some cuban rum at the airport when you land but whenever I travel, I "do as the Romans do" and drink the local drink, which in Nica, is Flor de Cana. There are numerous ages of FDC rum and are pretty good. I can't remember which age I prefer, but you'll have fun trying them. Of course you should try some good cuban rum too which I'm sure will be flowing!
The Legendario as Bill talks about is a sweeter rum and HC 7 especially has more bite. The older HC is more smooth. Just have guys buy different kinds and share until you find what you like.
When I was traveling in Nica by myself after the cigar guys left, my drink of choice was a Cuba Libre with FDC 7 year rum... rum/coke/lime.