I did a very similar route last year from NY but also dipped into Idaho and Wyoming. I took 3 weeks and felt rushed, total of 7200 miles. I think I averaged about 360 a day but had at least 3-600 mile days and a few 500 ones also. If you have the time try to make it a 3 week trip. I didn't worry about finding a place to stay until the early evening. Never had a problem finding cheap or free camping. I avoided the NP's for camping since most don't have showers or wifi. Private campgrounds seemed to be the cheapest and most had wifi. It's a great trip, don't rush it if you don't have to. Here's a free spot along the river just west of Boonesville, MO. I stayed there last year for a night. Harriman Hill Access - Booneville, Missouri River access with a primitive campsite. It is actually right next to I-70 but must be accessed by a 3 mile drive on Route M (paved) to the access. Location is a few miles west of Booneville, Missouri.