If you are keen for a bit of a walk and want to see some of the island head to the old homestead. You can get a walking map from the activities hut and it will show you diretions to the Homestead.
The walk is a fairly short one but I would recommend setting off early and taking lots of water if you are going in summer (when we went it felt like running in a Sauna!).
The old homestead is in quite good condition and even still has an old rocking chair on the balcony - across the mud-flats from the balcony you can just glimpse the ocean and when we went there were goats, peacocks and a few other little hen things about (they must have got away when the homestead was still in use). The resort claims that the homestead was built by a family in the 1920s who grazed sheep on the site for about 20 years. It certainly would have been an isolated place back then!
If you're up for a challenging hike, the trek across the island to the lighthouseis a great option. The "lighthouse" is actually a box like beacon, not some grand old style relic, but the walk itself offers fantastic views and an excellent opportunity to experience the Australian bush landscape. The walk begins at Fisherman's beach, the main centre on the island. You walk towards the airport, past the first lookout, then down past the homestead. On the way past the wetlands there is a turn off for the lighthouse. The climb from here is pretty rugged and largely uphill for a good while. Not being the fittest person in the world had it's advantages - allowing me to pause and appreciate the sights and sounds of the bush and the spectacular views of the ocean through the trees. As you approach the lighthouse thhe bush is replaced with a sparsley vegetated headland, with some very cool windswept trees and a beautifully rugged cloatline. The descent to the lighthouse is also fairly steep, and the wind picks up substantially (rewarding after the long walk). At the point there is a helicopter landing pad, the light beacon and a plaque with information about the light house origins. It takes about two and a half hours to get to the light house, making it about a 5 hour round trip (about 16 kilometres). If you do it in the middle of summer it may take longer with the heat making drink breaks more important.
If you're feeling adventurous, you can get off the beaten track and got down to Wreck Beach (aka Shark Bay) and then trek across the sand dunes and walk back via Svenson's beach. This is a long hot walk (it took us 8 hours with a few breaks). If you're not reasonably fit, i wouldn't recommend this walk, and definately not in the heat!
For any walks, make sure you take at least 1 litre of water with you, as well as a MAP, a hat and sunscreen. After our day of bush bashing, I ended up with mild heat stroke because 1.5 litres of water wasn't enough and climbing sand dunes was damn hard!! Do it wisely and have a blast!