It would provide shade and cooling effects - with sunshine from the north in winter if you plant a deciduous tree.
Citrus trees are good, not really prone to fruit-fly, too much. Or a nut tree - macadamia or almond - so you can accidentally feed some black cockatoo in a few years time.
There are a number of small Eucalypts and Hakeas that can fit in well in a garden. A few grasses and small shrubs can make a good little garden to provide habitat for local small birds.
Eucalyptus caesia is not a big tree, Euc forrestiana is another good one. Hakea bucculenta and Hakea laurina are also beautiful small flowering trees. Australian flowering trees are an important part of birds needs so a garden gets lots of visitors when they are flowering. The birds also provide pest control for any fruit and veg that are growing nearby.