Rob: You could fish Flat Creek on the Elk Refuge, it is on the north side of town on the right, it is your typical spring creek. Fly Fishing Flat Creek | High Country Flies
You could also wet a line on the Snake, take hwy 22 west out of town, it crosses the Snake river (Wilson Bridge), turn right and there is a boat launch on the right.
Also check with the local fly shops, there are probably other spots close by to wet a line.
If you can spare a full day, your welcome to come down and float the Green river with me.