Having the relative freedom to be able juggle my work hours and go camping at any time of the year and on any weekend I choose means that I can, if I wish, avoid the busiest and most popular times of the year when the school holidays kick in, and camp when it's much quieter. Although I do camp on bank holiday weekends when I know it will be busy I try to balance this out by camping early or late in the season and choosing sites which I know will be fairly quiet.
My regular site on Anglesey gets very busy to the point of being absolutely manic during late July and August, especially on the bank holiday weekend (think Glastonbury festival) but even then I can usually find a fairly quiet corner to pitch my tent. The two large camping fields at the Elvaston Steam Rally in July are very busy but I don't camp with the masses - I drive right across to the top end of the third field and pitch my tent in a corner well away from everyone else. That doesn't mean I'm anti-social - far from it - but with a very busy work life and a home close to a main road any peace and quiet I can get is very welcome.
Most of the sites I've stayed at so far, while always having that important quiet element, have still in some way had some form of background noise in the distance but there are four where peace and quiet are guaranteed - the site I stayed at on my very first solo camping weekend (no noise except sheep, hens, and birds in the trees), the camping field at the California site (nothing but the sound of the sea and seagulls),
the coastal site in the Scottish Highlands (sheep, birds, and gentle waves) and the one in the hills of North Wales where I recently stayed for the first time over Easter. With no tv signal, a very intermittent phone signal, and just the sound of the nearby river and waterfall and the birds in the trees it truly was quiet and peaceful - and at only two hours drive from home it's now at the top of my list of weekend escapes.