CloudDriver is correct, Prairie Dog State Park just west of Norton has several sites with electric and water. FWIW I live in Norton so I know a little something about 36 across Kansas. Low traffic is the truth but for RV'ing I view that as a very good thing. Once you get past Oberlin and on toward St. Francis the scenery changes a bit and you go from high prairie to almost-desert in some places. If you wish to stay on 36 once you cross the Colorado line be aware that there is almost nothing until you get to Byers and I-70. I remember driving that route once a few years ago (first time I had gone that way) and truly wondered if the world ended and no one bothered to tell me. Thank heaven for satellite radio!!
I think I'd do what some others have suggested: Turn north at St. Francis and get to US 34, then go west again into Colorado. More towns and some nice scenery around Wray.