Setting up the computer in the kitchen is a perfect solution for busy families. Many mothers and fathers would say they spend most of their time in this room, making it a great space to house the family computer.
The family room (especially if it opens to the kitchen) is ideal for electronics like TVs and computers. Your children can work on homework while you read or watch a show (with the volume turned down low, of course.)
If you tend to spend a hefty amount of time in the laundry room and the space has the square footage, consider placing a desk, a chair and a computer there. Your child can have computer time while you sort, wash and fold clothes.
Taking advantage of available space, like the wall in this mudroom, to place a desk can be a great solution. Your children can feel a sense of privacy all the while knowing you're not too far away to check in.
If you're still not too keen on having a computer in the common areas of your home but like the idea of monitoring computer usage, how about tucking a desk with a computer into a closet? When it's in use the doors are open, and when it's not you can close everything up and have it out of sight.