Flows normally are a challenge this time of year, but thanks to the amazing snowpack from this past winter, should be good right now. It's predominately rainbows and browns (some very large), but they do stock Lahontan Cutthroats in there. I had success basically anywhere from the Nevada line to the city parks in Reno, and upstream in CA should be better. The Little Truckee tailwater is also an option, nice high-mountain meadow stream.
If you were there after Oct 1, I would send you to Pyramid Lake. Just an insane experience, basically surf fishing for trout.
Otherwise, the Carson and the Walker rivers are up that way - never fished either, but may fit the bill for you.