My parents took me and my two* siblings on extended summer camping trips when we were kids. The most memorable were two summers in Europe. They bought VW Campers each time, which they shipped home. They sold the first one in the States, but kept the second and used it for North American trips for years afterwards.
The asterisk is because the oldest sibling spent most of the first summer in a camp in Switzerland.
These trips shaped my whole life, though clearly the idea wouldn't suit everyone.
The family on the second trip mapped yours pretty closely, as we kids were 14, 11 and 6 years old. My dad was traveling to Moscow to present a paper at a scientific conference. We spent a few nights in hotels here and there, and ten nights in a borrowed apartment in Prague while my parents worked to secure a Polish visa for my mom. (She had left Poland just after WWII. As a defector, she was no longer welcome in the socialist paradise. My dad finally resolved the issue by pointing out that preventing an eminent American scholar from delivering his paper would create an international incident and asking the consul whether he wanted to be responsible for such a crisis.)
Camping in Europe had a lot of advantages back then, many of which I think are still available. We had a great many interesting conversations with other travelers; we kids got to run around and burn off energy exploring new campgrounds every few days; in the Communist bloc, we escaped the bureaucracy that made tourism maddening for Westerners. That last bit is happily just history now.
The money saved on hotels made dining out more economically feasible. My memory is that we ate one meal a day in restaurants, but I don't think we really did it that often.