I don't have internet at home. Although it sounds horrible, it's working out better than I ever thought it would. With a bit of preparation, and assuming you have access at some point during the day, it could work just fine for you too.
There are two major things I do on my computer. Code and listen to music. I also check email way too much, but that can be mitigated. Granted, I'm not saying not having internet is better than having it, but you'd be surprised at how much you can get done without it (and you can argue, there are areas you can be more productive without internet).
If you're in my line of work, you can't avoid doing work at home. But if you get a good grip on setting up your work environment so that you can work completely offline, you almost forget you don't have internet. It's just once in a while when you google something, expecting Stack Overflow to come up as the first result, as it always does, when you think, oh, that's right. Then you go ahead and work on the thousand other things that need to be worked on.
I'm a heavy user of online music services, mainly Spotify and SoundCloud. If you're ambitious enough, you can download a lot of the music you listen to on SoundCloud to your computer, but I don't bother. For nine bucks a month, Spotify lets you download your playlists to your computer to play offline. That's incredible. There's a lot of music exclusive to SoundCloud but that can wait when I have internet for most of the rest of the day.
Admittedly, I'm not completely disconnected. I have an iPhone, although any smartphone will do. If you have to check your email, or you need your regular fixes of Facebook and Twitter, just do it on your phone. I like those last two's mobile experiences better anyway.
I also have a local copy of my email using offlineimap and Mutt. There's an unfortunate amount of information that lives in my email that might actually be useful even when I don't have internet, so I took an hour and followed this tutorial. Works as advertised. In fact, it's kind of nice to download all your mail before you leave the office for the day, spend some time at night with a beer or in the morning with a coffee writing your responses, saving them to be sent off when you get back to whereever you have internet.
The crazy thing is, with no internet, I might be even more productive than when I'm with. When I have internet, it's so easy for one of the million of distractions available online to catch your eye and to lead you off track. Nothing is there to catch your eye when websites don't load. It's just listening to music, and working.
And by working, I don't necessarily mean the work you do day to day. There are so many things we all want to do, be it side projects or personal ambitions, that involves staring at a screen. When you don't have internet, meaning when you don't have the opportunity to dwindle your hours away consuming random shit, the next thing that always comes to mind is the stuff you want to do on the side. Sure, I work on work, but I also built this entire current iteration of this blog offline. One of the best parts of side projects is learning and playing with new things so it might be hard if you don't have Stack Overflow at your fingertips, but if you're careful enough, before you leave your internet, load up some resources that will get you through the hour or two of work you have available at home and you will be good.
Here's something to try. Turn off your internet at work and work. You might be surprised at how much you get done.