Well, I was like this at one point. Actually, when i'd go on holiday my mum would have to take me to the only internet cafe 30 mins from where we were staying just so I wouldn't climb the walls. The first couple of days without the net can be hard but I promise you, after two weeks you won't be as eager to get online. I think it's down to the availability of the internet, people tend to use it because it's easy or because they are bored.
Use this bandwidth issue as a springboard, force yourself to go out and socialise, go shopping, go to a museum, anything. You will feel better!