There are lots of ways to get music, like Google Play Music, Amazon Music, Spotify, Slacker, Pandora, etc. These are either stores where you can purchase music to own, or streaming services that require a subscription. "Free" music download apps are usually shady, because unless you're talking about public-domain music, any current popular music that's downloaded "free" is likely pirated and therefore illegal.
iTunes music can be easily uploaded to your personal Google Play Music library in the cloud, which can then be streamed or downloaded to any device where you've logged in with your Google account.