There are great many options along the various highways and byways in the US for lodging, though if you are looking for B&Bs you would have to check ahead because they are usually small and may be booked.
When travelling on the interstates and other divided highways you would see signs like:
This one is to indicate that at exit 14B there is a HolidayInn Express. Of course you could see a sign which will leave you wondering:
But these are rare. Mostly along the roads you will find inexpensive chains like:
and a few others. Most of these are quite clean and safe to stay at though "mileage may vary".
One thing I would suggest is when you are travelling with kids is to actually plan out your route. For example, last year I went to a Finger Lakes region in the 2nd week of July and there was no hotels/motels/B&Bs to be had (except for obscene amounts of money) because of the local festival so check for those first and if possible make reservations ahead of time.