We've lived here all our lives. We like the west shore line of the L.P area way more than the East. Not that there aren't nice places there too. Your trip sounds like your taking the Western shore. Many have mentioned state parks. There are many excellent ones on your indicated route. However, starting Jan 1st they go up on the web for reservations six months out. Many are filled within weeks up to June. Starting Feb 1st July becomes available. It's amazing how fast the sites go.
If you have a rig 38' or bigger you aren't going to fit in many state parks even if they say you can, been there done that. If you aren't familiar with a particular park and you have a big rig it would be wise to ask people here. Making a reservation is almost mandatory at the popular state parks.