Interestingly, I feel like I've found more "new" music using Spotify's Release Radar playlist instead of their Discover Weekly playlist. I'll typically (and aggressively) mark things as like/don't like in those playlists and add what I like to my own "Testing" playlist to see what sticks to me. Release Radar tends to have more likes than Discover Weekly does, despite what the two are named, and it's providing new artists on top of existing ones I'm already a fan of.
That's usually good enough for me, though the occasional time I'm listening to the radio or a song comes on over the speakers when I'm out and about gets a quick Shazam from me to know what it was.