My daughter seems to be unable to click anywhere on the map and actually go there. She can go to her own house but is unable to go anywhere else (e.g. Unicorn Way).
Is there a trick or does her character need to earn the ability to travel?
Your wizard must travel using the arrow keys or mouse to get around, running and then later on getting a mount are the only means of transport. When you finish Wizard City areas you will be granted access to the World Door which is used to transport you between lands.
The map is just used for a guide on locations of things in the area you are currently in.