The book is about a teenage girl who lives on the Moon after aliens take over the Earth. I think there was a picture of a blonde girl sitting and the moon in the background on the cover. It was one of my favourite and I'd like to share it with my kids.
This Place Has No Atmosphere (1986) by Paula Danziger.
In the year 2057 people live in malls, take classes in ESP, and get detention from robots. Fifteen-year-old Aurora loves everything about her life. She’s part of the coolest group of kids at school and has just started dating the best-looking guy in her grade. Then her parents make the announcement that she’s sure will ruin her life—the family’s moving to the moon! What with water rationing, no privacy, and freeze-dried hamburgers, how will Aurora ever feel like she’s home again?