A long time ago we had a neighbor with a willow that covered his
entire backyard. From a distance it looked good, but the huge surface
roots made the ground unusable for most activity. He also had sewer
problems from the roots.

Drought conditions may limit your choices. But, willows prefer moist
soil conditions. You may want to test the pH of your soil--most
trees prefer slightly acid soils, others alkaline. Selecting a tree
is personal choice--I like ginko trees, in time they can get tall and
have a striking yellow leaf color in fall.