Not sure where you use this - never heard of it before and I have a lot of basil!

I'd lightly poach peaches in that basil simple syrup (diluted only slightly) to serve over vanilla ice cream for an outdoor dinner gathering . . . . with the syrup, of course. It would also make a perfectly lovely non-alcoholic spritzer. ;o)

Have a search on your favorite browser and make things you might like to have and to serve.
I found ideas for cocktails (alcoholic and not), sorbet, on vegetables or salads, to make ice pops, etc.