Music from Miyazaki/Ghibli films
In this video from 2008, Hisaishi conducts a live orchestra and chorus. Music featured from the movies Spirited Away, Ponyo, Kiki's Delivery Service, Nausicaa of the Valley of the Wind, Princess Mononoke, Laputa: Castle in the Sky, and Porco Rosso.
The Blu-Ray of this performance runs about $70 on Amazon. I don't own a BD player, so found the HD Youtube stream above.
Miyazaki & Studio Ghibli
I am a big fan of Miyazaki and Studio Ghibli films. The stories often mix fantasy with the daily Japanese life. What really ties the stories together is the beautiful music accompanying each film; often haunting and always memorable. Once I hear the film's main song I cannot help humming aloud for the rest of the day.
If you haven't seen any of Miyazaki's films then I would suggest starting with the movies below. Though most people will recommend My Neighbor Totoro, I find the three below more enjoyable. For most foreign films I believe the best way to watch and enjoy them is to find a copy with Japanese audio and English subtitles.
Spirited Away (music by Hisaishi) youtube
Howl's Moving Castle youtube
If you have seen these or wish to continue down the rabbit hole: Laputa, Nausicaa, Porco Rosso, Kiki's Delivery Service, Princess Mononoke, Castle in the Sky, Ponyo, Grave of the Fireflies, The Borrowers: Arrietty, and the famous My Neighbor Totoro.