You want safe routes to ride from the GSR RV park, 10-20 miles? Go either direction on the Tahoe-Pyramid Bikeway. West to Verdi, or east to Sparks. Go as far as you want and turn around. From the river near the GSR RV park, it is dedicated path all the way to the end of the trail in Sparks. Heading west to Verdi, from the river near GSR RV park, it is decidated path for maybe 2 1/2 miles, then mostly road shoulders, my best recollection is usually bike lanes, but pretty darned safe and not a lot of traffic. The only place that is steep at all is on a dedicated path close to Verdi.
I don't know how bad it is to get a block and a half east to the path from the RV park, but I assume it isn't bad, and it is only about a block and a half. I'm sure you can ask at the RV path the safest way to get to the bikeway.
You can go to www.tpbikeway.org
for more info, but if you're looking for safe 10-20 mile routes near that RV park, I don't know where you'd start besides that bikeway. I stayed at the Silver Legacy 3 1/2 years ago, rented a bike, took an afternoon ride to Verdi and back, and a morning ride to Sparks and back. It was good stuff, the least safe part was riding between the Silver Legacy and the bikeway, but it was tolerable, and the RV park is much closer to the bikeway, like I say, about a block and a half.