If you're planning on driving most of it rather than cycling, you can cover a lot of ground in three weeks. Easily possible. The only question is how much you want to see in each place.
Stonehenge is the sort of place that's fairly underwhelming for many people - it's not quite as impressive as you might think (what with it only being 18 inches high).
For scenery, and good walking (and cycling), I'd recommend the western highlands of Scotland. Good beaches too, although the weather may not let you enjoy them.
Nice Tap reference