I have discovered that musing about how your character would react in various situations is an interesting way to figure out more about them. Like how would they react to someone asking them on a date, or if they were alone in the middle of the city at night.
Also, things like what sort of sentimental items they have. Or random details about them,like what they like to drink with  breakfast in the morning.
good things to think about. I'm making a list of them for Lan.