How can I spend three Hobart days with a child without a car?

For kunanyi / Mount Wellington, consider the dedicated Explorer Bus rather than assuming a city bus reaches the summit. Check its current booking, weather and return options, and take warm layers even if Hobart feels mild.

Give the first day to the waterfront, Salamanca Place and a short Battery Point walk, with the Tasmanian Museum and Art Gallery as an indoor option. These sights sit close together, so you can adjust the pace to the child's interests instead of committing to long transfers.