You can find a lot of good music on SoundCloud. YouTube also has a huge storage of music in the "Studio" of your channel. You can use it absolutely for free.
We’re living in an amazing age with music. We have access to so much amazing stuff of all genres, but we can’t just lift it and expect people not to notice. I think it’s important that the artists get the credit they deserve, but I was a bit clueless about the whole process in the beginning.
For my first video for the bike manufacturers Inspired Bicycles, myself and the director Dave Sowerby used a track called ‘The Funeral’ by the US indie group, Band Of Horses. We didn’t know anything about licensing agreements and we didn’t think many people would watch the film. Once the hits on YouTube started creeping into the millions we got a letter from Band Of Horses’ label, Sub Pop. They were asking us to take the Inspired Bicycles clip down. That all changed when someone noticed that the video was acting as an unofficial promo for the band. Sales of the track had started to go up as a result.
You’re never going to convince someone like Justin Bieber or Metallica to allow you to use their music for free. And there are in fact a lot of sources where you can download specially-made royalty-free music. But my advice would be to scour around Spotify and find some smaller bands that you like, artists that are completely off radar. Contact the band via their label or management company and show them what you’re working on. If you’re lucky the band will like it. They might even allow you to use their track in exchange for a credit.