Pack a travel rod, some dries and small nymphs, a few indicators, some tippet, and head up to Crypt Lake (you need to take a FULL day, and a boat ride to the trailhead).
The scenery will leave you breathless, and the fishing is good for cutthroats. You do need a parks license for it though... which u can get at the visitors center on the right as you head into town (unless things have changed, and then you should be able to get it on the main street visitors center across from the ice cream shop)