Take a Day Trip: As with any travelling in a country as low a density as Perth, you will become accustomed to spending a lot of time travelling between the sights. One of the best day trips in Perth is to visit the nature reserve off the coast of Fremantle, Rottnest Island. You can access Rottnest Island by a ferry, 30 min from Fremantle or a longer from Barrack Street Jetty in Perth. The trip can be expensive, but Rottnest Express has a “Telethon Tuesday” deal with half price tickets ($35 instead of $70) every week for most of the year. Rottnest is a car free island, but plenty of bikes available for hire from the island or directly from the ferry company. There is a huge variety of wildlife to see (including the famous Quokka) and opportunities to see whales, dolphins and fur seals off the coast, but this will always depend on the season. Another (closer, cheaper but smaller) option is to visit Penguin Island, home of the "Little Penguins" or "Fairy Penguins", located 5 min off the coast of Rockingham, a 45 min drive south of Perth.
Cycle: Perth has excellent bike paths and fantastic weather almost all year round which makes it perfect for cycling. The paths that follow the Swan River are very scenic and mostly flat. You can take your own bike, hire a bicycle from one of the bike hire providers located near the Swan River or take a tour with Bluetongue Bike Tours or Pedal OZ.