E-bay would be my first choice for this sort of thing. I'd recommend a minimum of Pentium 166Mhz and 64Mb RAM for a very basic machine to run Windows 98SE. Check that it includes a working battery, but as batteries deteriorate over time, don't assume that you will get very long battery life out of it.
A lot of laptops had either the floppy drive or CD-ROM drive external to the machine, so make sure you are getting the drives AND connecting cables you expect/need as part of the deal.
Check also how you will plug into the Hotel's Internet access - it is via Ethernet, look for someone selling a bundle that includes a 10Mbps PCMCIA Ethernet card, or for a laptop that has a built in ethernet port (these were rare until fairly recently - expect to pay over £300 to get a laptop with a built in ethernet port). USB ports on a laptop are very useful.
Just don't buy a Sony...
(And let us know what you buy and and what price)