You dont need wireless, but it would be better, from the point of view of being more flexible. If you imagine a regular FM radio that you could only use in one location, then thats almost what you would get if you did not go for a wireless internet radio, in fact, you may as well just keep using your PC for internet radio.
If you dont wnat to go wireless, make sure the internet radio device you get has a LAN port. Otherwise, upgrade your existing router to a wireless one, and your flying (assuming the router will give you good coverage around the house, which in most houses is not a prob).
Wexfordman