There are a lot of cocktail uses for ginger syrup. The flavor goes great when combined with grapefruit or lemon. I use it frequently with rye or rum, but it goes well with other things, too. Experiment, and see what happens!
There are also a lot of non-cocktail uses for this syrup, too. For example, mix it with seltzer to make homemade ginger beer. Mixes well with tea. So many things to try!