Last July, I drove to Lake Tahoe for a wedding. Each day we drove 7-8 hours.
Left at noon, stayed first night in Helena MT. Next night in Twin Falls ID. There is a spectacular bridge over the Snake River Gorge there. This is where Evil Knievel attempted to jump the gorge in a rocket car.
http://www.roadsideamerica.com/tip/2961
Just upstream, Shoshone Falls are worth a visit.
http://en.wikipedia.org/wiki/Twin_Falls,_Idaho
It is another full day drive from there to Reno/Tahoe. There is a small gambling town as you just cross the border into Jackpot, Nevada. Not much to see in Northern Nevada except antelope.
Reno is a relatively big city now. 700,000 metro. I did not go to the casinos, but there is a large outlet mall in Sparks, Nevada.
http://en.wikipedia.org/wiki/Reno,_Nevada
Lake Tahoe is spectacular, and worth visiting for a couple of nights. There are beaches, but the lake is quite chilly for swimming. It can be expensive - many wealthy Bay Area people have weekend retreats here. There are casinos on the Nevada side of the lake,
http://en.wikipedia.org/wiki/Lake_Tahoe
On the return we went back to Twin Falls. From there to Teton/Yellowstone - it is a full day to drive around the park and see the main attractions. It is crowded and traffic is bad.
http://en.wikipedia.org/wiki/Yellowstone_Park
For flyfishers - you will drive by plenty of great trout streams in SE Idaho, Yellowstone and Montana.