Mount Rose is spectacular. It's moderate difficulty. I'm not sure whether there's a designated trail. You just go up as you can. Near the top, things sort of converge upon a single trail.
Besides Mount Rose, there are innumerable other great trails and hiking opportunities around Tahoe (which is right next to Reno). Tahoe Rim Trail, Dick's Pass, Shirley Lake, Tamarack Lake, Granite Chief Wilderness, etc.
Note that the area is fairly high, and there will likely still be a lot of snow, if you go around Lake Tahoe anytime soon. The lake is about 7,000' elevation, as I recall, and Mount Rose is 10,077', IIRC.
