Yes, it's the legendary "Let's Go to the Mall" by Robin Sparkles. (Thanks to Alan Sepinwall for pointing this out.) "How I Met Your Mother" fans will note that Robin Sparkles was, in fact, "HIMYM's" Robin in her younger days. But you don't need history to appreciate the sublime, perkalicious '80s quality of the video.
And, just because you can't listen to that song just once, here's a version with paper-bag puppets:
Stay with it. Some great cat socks near the end.
And, just to remind you of the roots of "Let's Go to the Mall" (and the great detail in the video) here is Tiffany's mall-hopping epic "I Think We're Alone Now":