Cross-country trips are tiring, and you'll be anxious to hit the sack every night; so, it's a good idea to have lodging reservations in place well before you leave home. Hotels, motels and even campgrounds fill up fast in popular tourist areas, especially during prime vacation season, and some places sell out months in advance. Once you've targeted the places you want to stop each night, make reservations.
A few days before you leave home, call each place where you'll be staying to confirm your reservations, and bring your confirmation information with you, too. That way, if the hotel loses your reservation and is full, you have proof with which to demand a room. (And they almost always have extra rooms.) If they truly don't have space, hotel staff should find you a spot elsewhere because they've erred.