Tony

Answer: He could have looked up her address in the phone book. Just before Bruce arrives at Vikki's apartment, Joker asks Bob the Goon for - a phone book. Also he could have been tailing Bruce and found her apartment that way, after all he does show up not long after Bruce does.

Alan Keddie

Chosen answer: She's a semi-famous reporter/photographer. It would be fairly easy (especially for a criminal) to find her home.