The original song is from Puella Magi Madoka Magica. It acts as a character song for the title character, Madoka Kaname, and was sung by her VA, Aoi Yuuki. Full credits can be found here. This translation was based off of several others (mostly this one and another official one in the subtitles) I had seen to get the general idea and meaning, and only covers the first part, used in the outro.
I claim no credit to any part of the song; I just wanted to see if I could put together an English version that fit the melody. I will probably regret posting this.
I'll wave goodbye to you, say "See you later,"
Smile like I mean it as I watch you slip away
[Instrumental]
Car engines and bicycle bells
Chat and gossip from across the street
Traffic and road noise and the laughter of
Some people I don't know
As I walk alone through the city today
It seems like nothing should have changed
But the buildings tower over me
And I can't help but feel I'm smaller than I was before
I'll wave goodbye and I'll say "See you later,"
Make my smile a mask that never slips or cracks
And holds back all the useless questions I wanted to ask
I'll wave goodbye to you, say "See you later,"
Even if we both know you won't be coming back
But with this same old smile, I'll lie and say that I'll
See you tomorrow