I'm going to do the unusual, and answer my own post, sharing a great solution that a friend identified.
Take a look at this nifty ethernet adapter that slides into the CF card slot on the Axim. You just plug a standard ethernet cable into this adapter, and plug the other end of the ethernet cable into your hotel room's ethernet jack.
http://www.socketcom.com/product/EA2917-722.asp
I discovered on Ebay that the US military had purchased a large quantity of these, which were used briefly by officers and then no longer needed so they sold them to (or contracted with) some small firms that are selling them via Ebay. The ruggedized typically goes for roughly $30 (used) and the non-ruggedized version (dongle can be removed) goes for roughly $25 (used), on EBay.
I bought one used and it works great with the Axim PDA. Be sure to download the latest drivers from
http://www.socketcom.com/.
If you have any problem finding this on Ebay, feel free to write me
stephanvrudny@hotmail.com, and I'll forward the email of the company that sold me one used for $25
Stephan
San Diego, CA