I immediately thought of
Fellowship of the Rings - which is my quintessential ‘over the hills’ book. Lovely wafts of nostalgia.

But as gmw said about
The Hobbit, everyone who wants to read it, already has.
Several of the old classics, like
Huckleberry Finn come to mind, but I’m afraid they haven’t aged well. I’ve read several articles on the best adventure books, etc, but nothing quite fits. So I need to do a bit more thinking too.
Charlie, fwiw, I think the space operas would fit the theme very well.