Even though you've given us some idea of things you like doing this is going to be a very difficult one to answer because... well, you're basically saying something like "What can I do or see in a 300 mile radius of Heidelberg?", which covers a fairly large chunk of Germany plus several neighbouring countries... there is so much to do, and so much to see, it's going to be quite difficult to suggest particular place as there is so much choice.

You could go to the Black Forest. You could go to the Alps. You could go to the Alsace region in France, or the Ardennes in Belgium... or you could go to any of a number of major cities within a 300 mile radius including Paris and Prague.

If you particularly want to drive (rather than take the train) then how about picking a destination that's maybe 150 or so miles away, and take your time getting there and explore a few places along the way? You could pick Strasbourg and drive along the Rhine. You could pick Basel and drive through the Black Forest. Just a couple of examples