It's Latinized, so classically it should be somewhere along the lines of AH-stry-a. I think it's lovely and the meaning and story are nice. For a middle name I like something short and sweet:
Astraea JuneAstraea MayAstraea JoyAstraea CelesteAstraea LilyAstraea LaureAstraea WrenAstraea MaeveAstraea Lenore