NPCs not involved in the main story can tend to be overlooked but they add a lot of flavor. Here are some of my favorites.
Quotes sourced from Poké Corpus.
First off are the various NPCs in Pokémon Black, White, Black 2, and White 2 that play instruments or sing. I might detail more in another post about the history of voice acting in Pokémon games. It goes back to 1998!
The first two NPCs that play music are in Accumula Town in B/W. They are siblings, one of which plays piano and the other drums. These instruments will add on to the regular background music of the area. Though if you listen to their tracks isolated it's sort of weird! What kind of song is the piano girl playing, where you only hit the keys every few seconds? If we're assuming that the background music in this game is non-diagetic (the characters can't hear it).
"My! Heart! As long as my heart beats! I will keep! On! Drumming!!"