It shouldn't be $60 a night once you get out of the East, until you reach California where high land values push rents back up into the stratosphere. Everything in California is expensive, just like everything in the D.C. to Boston Megapolis is expensive, but it is not that way in the rural middle of the country.
Through most of the middle of the country the RV parks serving travelers have been in the $25-40 range for me, the lower number overlapping fees in the nicer state parks, and not much higher than fees for Corps of Engineers properties (although you might be eligible for 1/2 fee camping on the Access pass. State parks generally, the more complete the facilities, the more expensive they are.
We used to travel without making reservations ahead of time. This means avoiding weekends at popular recreation areas near cities, in season, and avoiding urban areas generally (because high real estate values mean either high rents or no RV parks at all). I think this has gotten more difficult as more and more public facilities are abandoning their "first come, first served" policies and catering to a new generation's expectation that everything needs to be reserved.
Because reservations for a whole trip don't fit our flexible mode of travel, what we usually did was figure out around noon where we would be at the end of the day, look up facilities that distance out, and call for reservations for that night. This works for commercial parks, not so well for public parks, which tend to require reservation 24 to 72 hours in advance, partly because of communications issues between remote locations and a central reservations system.
When we did this in the 60s (family of six children, my parents and grand parents) we just pulled in somewhere to sleep at the end of the day: sometimes parks, sometimes city or county campgrounds, sometime RV parking at gas stations. Hookups weren't necessary, our travel trailer was essentially self contained and self sufficient for how we were using it, i.e. alternative to a tent. However, if what you want from a RV is a modern house on wheels, it is harder to do that without attaching to the grid. Only larger, more expensive RVs are self sufficient at that level.
