How did he have her address ?

She told him off-camera. After she left after the second encounter, Kendrick asks “Where does she live?” Clooney said Chicago. So she told him off camera.

When she went to the wedding in Wisconsin, he dropped her off at the airport, where she boarded a flight to Chicago.

It’s also possible that she didn’t tell him the exact address, but he check a phone book or something, as he knew her real name, phone number, etc

I thought it was explained that he looked at her suitcase's tag. Airlines still hand you little tags to write in your name, address, and phone number. Even for carry-ons.