Try Feedly. As best I can tell, it's the only spiritual successor to Google Reader from years ago (I'm still salty Google killed it). It's about the only worthwhile non-self-hosted RSS reader online. Being online, it will sync between devices.
If you're a little more technically inclined, you could also look into self-hosting your own feed reader. That's beyond my abilities, so I don't know where to point you for that.
Out of curiosity, how do you manage to follow so many feeds? I've been using RSS for probably 20 years now, and feel like I easily get overwhelmed when I get over a dozen feeds or so.