If you're taking your PS2 on the road, you might want to use the hotel's wireless network connection to play online. Is this even possible?
First off, it is critical that you read and understand my page on how a PS2 connects to the internet. PS2 Online Connection Information With Diagrams
So your PS2 needs to have both a network adaptor, so it can "talk internetese" as well as a wireless object so send that language over the airwaves to the hotel's wireless system.
The issue here is that the wireless object needs to be CONFIGURED to work with the wireless network to which it will connect. It doesn't just "know" who to connect to. Usually, you have to plug your wireless object (your Linksys bridge, for example) into a PC in order to do that configuation. So you'll need to bring along your laptop and the appropriate drivers, in order to do that configuation. The hotel will of course tell you what settings to use.
A card won't do any good. Cards are items meant to plug into PCs. You don't have a PC here with a card slot - you have a PS2. The PS2 takes in normal ethernet plugs :) It doesn't take in card slot items.