Known to the Chinese as Guihua 桂花, coincidentally I have a friend named the same. These clusters of tiny yellow flowers will surprise you with their intense floral perfume. One sniff will turn you into a fan of this Guilin native. It is only there that you can obtain a myriad of items made with this poignant bloom, including a bottle of chinese osmanthus perfume.
I didn't get the perfume but I did buy their famous 3 flower wine, recommended to me by a shop proprietor. Each region brews it's own spirits and in Guangxi, this is infused with osmanthus flowers, creating a strongly perfumed 50% alcohol spirit at 20 RMB a bottle. An affordable treat for anyone visiting this region.
Then there is osmanthus tea that is plucked in season, this means it is not always available. A sweet floral scent is released the moment it is brewed and is one of the few chinese teas that can be served with milk and sugar. If you are still at a loss, then just get a packet of osmanthus flowers. The local restaurants sprinkle it on top of steamed fish and use it to make desserts (e.g. jelly, dragon's beard candy).
The only beverage I would warn you about is the osmanthus wine that is exceptionally bitter. Only one brand makes a decent version of it.