There are some places in the game where you can sit down and the music will slow down as the camera pans from one side to the other from various angles. It doesn't seem to serve much purpose besides that. Are there any seating places where something different happens if you just sit around for a while? Or is that really all it does, no matter where you sit down?
The chairs serve as a scenic overlook to the levels. There is no gameplay benefit or (known) Easter eggs tied to the chairs.
However, as a non-gameplay benefit, to obtain the achievement “If I fit, I sit”, the player must sit in three separate chairs.