Kyst til Kyst Stien is the coast-to-coast route that starts around Vejle Fjord and cuts west across Jutland toward the North Sea. It is not a quick city walk, but it gives Vejle a proper long-distance escape: forest tracks, open farmland, river valleys, and small Danish villages rather than another lap of the waterfront.
You can sample a short section from Vejle if you only have part of a day, or treat the route as a multi-day hike or bike trip with overnight stops along the way. The appeal is slow travel rather than spectacle; bring maps, rain gear, and realistic expectations about distances between services.