In the earliest Batman comics, Bruce Wayne dates the often-imperiled Julie Madison, an actress and socialite who eventually weds into European royalty, much in the manner of Grace Kelly. Julie first appeared in Detective Comics #31 (September 1939), only four issues after Batman's own debut.
Located on the outskirts of Gotham, Arkham Asylum is a psychiatric hospital where many of Batman's foes are sent for rehabilitation. Unfortunately, Arkham doesn't have a very good track record. Inmates escape on a regular basis, and those who are discharged often return to a life of crime.