For an overview of the Aboriginal, natural and pioneering history of the Karratha area, you could start with the Jaburara Heritage Trail. It begins in town but extends to include a few steep climbs and descents and you'll need about 2–3 hours to complete it leisurely. The 200,000-hectare Millstream-Chichester National Park is a 2-hour drive inland, offering beautiful camp sites amid gorges and rock pools.
Out on the water, the Dampier Archipelago comprises 42 islands and gives you the chance to dive, fish and snorkel in pristine waters. You can camp there as well. It's also a nesting site for various species of turtle – and dugongs, manta rays or bottlenose dolphins might visit while you're there.