I went across the US two years ago without any plan or route. I just wanted to get myself home quickly and under my own power before summer ended so I was averaging about 90 miles a day. Most days I would try to ride 100+ miles, but I also had a few short days and bad weather days that dropped that amount. Don't listen to the naysayers. I would say any sufficiently motivated young healthy person can average 100 miles a day over the summer. The limiting factor will be if your butt or knees break down or if the days are short and you run out of sunlight.

For the route, I would stop in at libraries and check Google maps and emails every few days. I tried to cut a straight diagonal across the US. I had a pad of paper I would jot down highway numbers and towns that I should cross.

As for camping. I mostly started looking for a site when I noticed the sun was getting close to the horizon. A few times I never found anything I would call a campsite. Mostly that was in ranch country where there were no trees around and all the property was fenced fields. One time I slept under an abandoned rail car. One time I slept in a large (and dry) culvert under the highway. It was actually pretty nice with a fire inside. And more than once I just rolled myself up in a sleeping bag and tarp in the ditch next to the highway.

The longest uninhabited stretches (without stores) I came across were around 70 miles and those were rare.