Conejos River for moving water is just about 15 miles west of town. Brown trout water. Hit the obvious holding spots, make a few casts, and then keep moving. A great river that's finally back after the drought years.
For still water fishing there's Platoro Reservoir which is a good 30 miles west of town but great fishing. And a coupla lakes above the inlet of Platoro too.
Plenty of high lakes come to mind like Bear - but the exact names escape me now. They are all south of the road as you go to Platoro and, if I remember correctly, are in the South San Juan wilderness area.