Great place to base out of, as mentioned there is alot of great water in the area.
Most of the places I would hit have been mentioned, if your willing to travel about an hour and a half north up towards West Yellowstone you could hit 'Hebgen Lake' and fish for gulpers in the early morning hours, monster fish that cruise around looking for Calibaetis emergers and adults.
Best fishing being from sunlight till the wind comes up, usually around 10:00/11:00.
Typically you need a boat of some kind, the object is to spot a riser and cast where you think he will come up next, can be quite challenging.
If your in that area you could spend the afternoon fishing the 'Box Canyon' of The Henry's Fork, and the evening fishing Rusty Spinners on the 'Ranch' section about 3-4 miles downstream, not the easiest of waters to angle as the fish are educated by some of the best Flyfisherman from around the world.
Hope this helps you out.
If you decide on a guide, let me know, I know some good ones in that area(West Yellowstone, Henry's Fork, and South Fork), you may want to consider hooking up with Davo for the area's closer to Driggs or Jackson, I think he would take good care of ya.