Things To Do in Exmouth July 23, 2020 Laura Waddell Exmouth beach. Watersports hire available in along the seafront. Out on our kayaks, in Exmouth Estuary. Queen’s Drive Space, just across the road from the beach Exmouth’s Jurassic Play Park Some of the Dinosaurs you’ll find on Exmouth’s Dinosaur Trail One of the dinosaur brass rubbings Phear Park The old railway line that leads to Phear Park.