We take this drive to Florida every March Break and usually just book hotels as we go. Once we cross the border into the state where we plan to stop and sleep, we stop at the welcome center there. They always have coupon books at the welcome centers and, if you arrive during business hours, they have very friendly staff that can provide advice and even book a room for you.
When we drive down we're usually just looking for a place to grab a shower and a quick rest before getting back on the road and have found Super 8, Motel 6, and Knight's Inn to be the most economical and clean enough for a short stop. Their free breakfast usually consists of a few pastries, a selection of coffee/juice, and mini cereal boxes so if you're looking for more of a buffet-style sit-down meal, this might not work for you.
Good luck with your trip planning!