Also google Flying J Truckstops on your route. That will take care of at least one or two nights of your journey.
You can park for 'free' in their 'RV' parking lot. Right next to store. No purchase necessary, just pull in and park.
All the ones I have stayed at were very nice and very safe. Food and bathroom facilities right there. Most of them have PLENTY of grass and trees to walk the pets too!
AND this time of year you will be surrounded by a plethora of other snowbirds doing the same thing! Actually I found it a pleasant place to spend the night, exercise the dogs and sleep in my own RV. They are right on the interstate easy off and back on if you want to get an early start back on the road. :C