The only issue you face is if there are several WiFi networks in the vicinity. Then how doe the repeater know which one to 'repeat'? With the Linksys, when you switch it on initially (there's a reset button) you place it close to the network you want it to repeat. It monitors all the WiFi signals it can receive and chooses to repeat the strongest one. Then you move it to an appropriate location. So, you might initially need to take the repeater down to the hotel lobby so that it can find the appropriate signal to repeat. The problem I can foresee, however, is if the hotel has a number of 'private' WiFi networks. If you simply sit in the hotel lobby, it's possible one of those private networks might be stronger. So, unless the hotel lets you place your repeater temporarily next to the free WiFi base station, it might pick up and repeat the incorrect WiFi signal. But that initialisation only takes a few seconds. Download the Linksys (or other) repeater User Manual and see what you think.
Tim