Zephyr Cove, as well as Meeks Bay Resort, are nice places.
Here is what you need to know. Cave Rock tunnel on highway 50 to south shore is a beast. You need to be right down the middle of the two lanes, on your side, whether heading north or south.
This is heading south...
If you have to, just wait until you are the only vehicle. We have made this trip many times and some times I have just stopped in the slow lane and put my hazards on until I could take the center of both lanes.
If in October, remember that while we often have Indian Summers, meaning nice weather, we can also have snow, especially at 6200 feet elevation.
If you want to stay in Reno, or more appropriately Sparks, try Sparks Marina. Reasonable and nice.
If it were us, we would stay some time in Sparks to enjoy what the Reno/Sparks area has to offer (our home town), and then head up to south shore, weather permitting.
Oh, and if you stay at the KOA in Salt Lake City, make sure you have a pressure regulator. Their pressure is 100 psi!