Some years ago, we did something similar with our dog. She was a great traveler, loved car rides, and we enjoyed our road trips through our dog's eyes.
When we were just staying a night somewhere, we made sure to find hotels that were dog-friendly and booked them ahead of time. Be aware though, "dog-friendly" does not mean all dogs. Some hotels have dog breed or weight restrictions. Also, extra fees if you bring your dog. I also would use Google Earth to see the area around the hotel to make sure there was a good place to walk my dog. Being cooped up in a car for hours at a time means I had a dog that needed nice long walks/jogs to burn off some energy.
In Florida, we used the Best Friends kennel at Disney and then drove to our cruise in Fort Lauderdale. When it came to picking a place in an area we were not able to visit ahead of time, I decided to go with a chain that I was familiar with, and I felt comfortable with Best Friends. This was about 8 years ago though, but I assume they still have a good reputation.
Another option, which I did not know about years ago, was to go on a place like CityData and go to the forum in the area you are considering for a kennel. You may be able to find some recommendations from locals there.
We now have two dogs that we take on trips with us, and while it may be so much easier to just hop in the car and go without our dogs, we bring them with us anyway. The love for life that dogs have, no matter where you stop with them, just makes road trips something enjoyable rather than just a way to get from A to B. Good luck, and have fun!