The first website you can try is our favorite [url]youtube.com[/url], but as you know there you have only two options: pay & listen, or listen music & ads
Maybe Spotify is the thing you need. It has much less ads but sometimes it stops you from skiping song (you can skip only 6 songs per hour in free spotify version)
Also, I have discovered another music service called feelmp3. It was a radio I used to listen but than it moved to web-based concept. They have just started, I still wait for their application for mobiles.. But you can check up beta-version here:
https://feelmp3.com