A full day in Fremantle covers the historic strip — prison, courthouse, Round House, then the Maritime Museum and Shipwreck Galleries on the harbour — with lunch at the Fishing Boat Harbour and a walk down the Cappuccino Strip in the afternoon. The Friday-to-Sunday Markets are unmissable if your visit falls then.
With a second day, the ferry to Rottnest Island is the obvious choice. Other strong options are the Swan River cruise to Perth, an hour at the Fremantle Arts Centre, and a sunset walk to the South Fremantle Power Station ruin or up Monument Hill to the war memorial.