I would say the Perth Arena has many low budget options. Then again it really depends on the budget. If you are looking for free, you just need to walk around freemantle and drive along the coast to enjoy a day out!
The Art Gallery and Museum are free. You can watch pulled candy demonstrations at RocCandy and get free chocolate samples at The Margaret River Chocolate Factory in the city. Or pack a picnic and catch a CAT bus to Kings Park for lunch and a look at the beautiful cityscape.