Where can I find free music websites?

There is definitely no website where you can download absolutely anything legally or safely. However, there are places where you can stream absolutely anything legally. There are also other places where you can download free legal downloads of songs from bands who are promoting their album via free give-away downloads of album tracks.

Streaming music for free

Myspace still exists and represents a method of streaming music from your favourite bands or band that you just want to listen to as a musical discovery. However, it’s not as reliable (in terms of a non-interrupted stream) as other sites.
Soundcloud
Soundcloud is probably your best option in streaming music, especially as bands often choose to stream their albums there. Now that Spotify have cut the amount of hours and plays during which you can stream music for free, many people are turning to sites like Soundcloud. It’s also a place where new bands tend to give away downloads of early demos or exclusive album tracks in the run-up to an album release. Therefore, as well as being free, it’s a great place to discover new music and listen to music by established artists online.
Bandcamp
Bandcamp also works in a similar way to this but it's only possible to listen to one track at a time. It is a website which bands use to stream, sell or give away their music. It is mainly used by new bands as independent market tool.

Downloading music for free

Bands tend to use the following methods when giving away their music for free: Soundcloud, Bandcamp, and occasionally file sharing (downloading) on websites such as Mediafire. They may also give their music away when people sign up to their mailing list.
A web-based following In order to find out when your favourite band is giving away a track, you can follow them on Soundcloud, join their mailing list (this is probably your best bet), 'like' them on Facebook or follow them on Twitter. Music websites If you're more interested in downloading new music for free on the internet, then your best option is to follow music websites/ blogs. You will be able to read all about the best new bands and find out when they're giving away Mp3s. Many new bands do give away free Mp3s to real people into their music.
Mailing lists It's a matter of opinion as to which are the best music sites but some of the most popular free music blogs are probably Neon Gold, My Band's Better Than Your Band and The Pigeon Post as they're constantly giving away free new music. However, if you're looking to get in on free downloads from established artists, then just join their mailing list.