In an interview with Pandora Billie Joe said

We booked a mini-tour and we had to drive all the way out for, I think it was for like 36 hours to South Dakota. Everyone was wondering why we were playing five shows in the middle of nowhere but it was basically to meet a girl I met up with her in South Dakota, but we ended up playing in Mankato, Minnesota, Minneapolis, and I think like Baloyt was concent so…

And then I wrote a song called “2000 Light Years Away” which is about the girl in the song who eventually became my wife.

He told Rolling Stone

The first tour that Green Day ever went on, I met my wife, Adrienne, at a house party in Minneapolis. She asked for an address because we had run out of our vinyl. Then we started corresponding and kind of became pen pals, and having these long talks, running up phone bills.

Then Green Day booked this mini-tour. We drove from California all the way out to Minnesota. Nobody really knew why we were driving all the way to Wisconsin and Minnesota to just play, like, four shows, but I was really just going back to see her. On the way back, I wrote “2000 Light Years Away.” The song just wrote itself. I put it down on an acoustic guitar and sent her a cassette of it. When you write a song for a person that you’re falling for, you don’t know what the response is going to be. The last thing you want is for someone to go, “Oh, you’re a stalker!” But it’s been a staple in our set ever since, and it led into many, many, many songs I’ve been writing about her for the next almost 30 years.