From Serbia to Karlštejn without crowds of tourists

The landscape around Karlštejn is picturesque and the views spectacular. But when we follow the tourist sign and it's not raining, we're actually always in a crowd. I am one of those people who enjoy the company of other people a lot in Prague, so on the weekend I go somewhere where I can be alone with my family and not with half of Prague. So I mostly avoided Karlštejn and its surroundings with my children, until it occurred to me that there must be...