One of these days you will be loading up your favorite waste of time, look at it and go "no, I've got this other thing to do."
Its not that productive tasks are boring or unrewarding, its that you, in all likelihood, don't find the material all that interesting. Hence the internet. Its not that the content on the web is low-effort, low-reward, its that the content on the web is a thing to do. Its mental snacking; you're bored, so you snack.
I've had this issue too and I'm starting to really get off it. I look at a lot of sites now and they've become boring, and the way I've accomplished this is by doing things that I find interesting, whether that's video projects with friends, directing scenes for director's lab, working on tabletop systems that'll probably go no where, or just doing something I find entertaining.
But its not really the internet's fault, you just need to find something you love to do, and then do something new with it, even if its dumb. Like playing piano? Write your own music. Already writing your own music? Make an album, cover songs, start a band. Never keep the envelope on the desk. I've been working on always trying to push that, and I've found I've been happier, more productive at home and work, and generally a less stressed person.
Once you find the thing you love to do, then the rest will be a lot easier. Humans are really good about that "meaning" thing that we all like to have, and giving your life meaning through a task is an easy way to get it organized. Speaking of which, I've got shit to do before work.