Maybe try serviced apartments in East Melbourne or along St Kilda Road so you are near some of the parks. The Botanical Gardens are good - check out the Children's Garden. Watch and feed the ducks. Haven't been to the zoo in a while but every small person I know loves it. Kids under 15 are free weekends, public holidays and school holidays. If you have a membership at your city zoo you might have reciprocal rights for free entry. Catch the tourist tram around the city - it's free. The Museum has some good kids stuff - check it online.