I have never found that RVing is cheaper than car and motels. We do both and the vehicle we take depends on the sites we want to see and what we want to do.
It costs us up to $150 to fill up the gas tank on the RV and for $150 in the car we can go four to five times further (but our Honda gave us 40 MPG and our RV gives us 11 mpg)
When in the car, we never spent more than $110 for a room at night and that was only once, most of our hotels ran between $60 and $85 a night and that included breakfast. So we only had to buy one meal a day and snacks for the car. So if your doubling it, your spending $150 a night for motel and breakfast.
When we take the RV we still have to buy food to cook and there is the hassle of expecting someone who has driven all day to now cook a meal. Believe me, its not fun.
If you make reservations for the motels you will get a better rate than if you just go in cold. Before our trips, I decide where we want to stop, I google the motels in the area, pick out two with the best bang for the buck with the best reviews, and jot down their address and phone number. I make reservations for the first night and when we get to the motel, before going to bed, I make reservations for the second night. I have found that if the town I want to stay at all the hotels cost more than I'm willing to pay, I just go to the next town and check on prices there. Its amazing the difference. Smaller towns seem to have been deals on hotels than big cities.
I find that driving an RV is also more stressful than a car so there is that to consider also.
What ever you decide, happy travels