Out here on the west coast service-connected veterans can camp free for 20-days at each State Park, and California has about 300-State Parks. Oregon also allows disabled veterans to camp for free. I would check various state recreation websites along your route to see if they have camping discounts for military veterans.
You might also be able to get a Golden Access Pass to camp for half price at National Parks. I think you have to be 62 or over, but lots of States also have Senior Citizen camping passes.
As far as military base camping is concerned, at Travis AFB in California you can stay up to 6-months (180-days) each calendar year. Beale AFB in California allows up to 4-months each calendar year. So it varies. According to the military campgrounds website California has more military bases than any other state and most of them have excellent Famcamps with free wifi, cable TV hookup at each site, etc. The Navy Famcamps are usually right next to the ocean.