Don't Sleep in Rest Areas
Pat,
In most states, sleeping in a car in a roadside rest stop is illegal, beyond that it is the surest way to attract problems. On those nights where you are not staying at a motel or hostel -- consider the (auto) parking lot at Truck stops. Much safer.
You have a great route mapped out. Should be fun. However, 350 miles per day does not allow for much time to get out -- smell the roses and take walks to the areas you will be driving through. In the national parks, you will find it darn hard to travel 350 miles in a single day unless you plan to be on the road 9-10 hrs/day. Speed limits are lower and there are so many places to stop and ogle at that you should figure that an average speed of 35 MPH will be the fastest you can go.