Givskud Zoo is an entertaining safari park with plenty of African animals, and you can explore certain areas from the comfort of your own car or in the park-run safari buses (40kr). Walking trails will take you past elephant and gorilla enclosures; for littlies there’s also a petting zoo.
Check the website for closed days; note that closing times vary (from 4pm to 8pm). Bus 211 runs regularly to the zoo from Vejle, via Jelling.