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Although I'm sure that others have differing opinions, probably your best value for the money in camping are state parks. I'd start by getting a good road atlas of the U.S., picking a route, and then decide roughly where I'd like to break up each day. We generally recommend 500-550 miles as a solid day's drive, but you'll have to keep in mind the added time to set up and take down your equipment each night. Once you have a rough idea of where you'll be trying to camp, look for the 'park with camping' symbol (usually a tree & tent) and then look online for that park's website to see what amenities such as showers, stores, etc. it offers. If you really want to rough it on occasion, look for national forests near your stopping points, check their websites and see if they offer distributed camping, which is really just 'roughing it' away from the roads and away from established campgrounds, cheep but NO amenities.
By the way, Baltimore to Chicago is probably too far to drive safely in one day, even with three drivers. Also, you may want to consider staying a little south of there and using I-70/I-74/I-80/I-29 as an alternative to using I-80 which is a toll road through much of the Great Lakes/Midwest. Also, how many days total do you have for the trip and is it one-way or round trip?
AZBuck