Lose the Computer Room?

Now that my daughter is entering the 'tween' stage, I am seriously considering moving her computer downstairs. Right now, all the computers are in the computer room with the exception of my notebook which is in the kitchen counter. We use a wireless Linksys router so I'm still connected to the internet. Back to the kids' computer, since we all hear about these horor stories of kids and the internet, I want to be able to monitor their computer use. She doesn't use any chat programs and she's not in any social networking sites. She's not interested and even if she is, I won't let her use those. I don't know how long I can keep it this way but I want to take all precautions necessary.