If your preference is close to Snowmass, has fish and easy access, I suggest Jaffee Park on the Roaring Fork. The fishing at Jaffee will probably be quite good but, with runoff, fairly difficult. Again, I suggest this only if you want something close and with easy access. To get to Jaffee Park from Snowmass Village: take Brush Creek road to intersection with Highway 82. Turn left and go about 1/2 mile to Smith Hill Road. Turn right, go 300 yards or so and you will cross the river. Immediately after you cross the river, turn right into Jaffee Park parking lot. You can fish around the parking lot or walk upstream as far as you want.
Another 'close' option would be Snowmass creek. However, to fish Snowmass creek you'll have to consult a fly shop for info on access. Sorry, but I don't know if there is a fly shop in Snowmass village. This may be too difficult an option.
If you want 'best bet' to catch fish, I agree with Meadowlark......go to the Frying Pan. If you choose to fish the pan, stop at Taylor Creek Fly Shop
in Basalt. Tell them you want to fish the area between the 12 mile marker and the dam. Tell them what you want to do and they'll get you rigged. Guys in the shop are friendly and helpful but don't expect them to be too free with info on where to fish. Check their website for fishing reports before you head out.
If I were fishing the pan today, I'd start at the 12 mile marker. Easy parking right next to the river. There is a big hole right in front of the parking area. Guides pound this area.....because lots of fish and easy to catch. From the 12 mile marker, work your way up stream stopping at every spot you can park. Keep moving.
Hope this is helpful. Good luck!