It's good that u are able to go online with the wireless router but one thing unclear here is that are u going online by the wired medium or wireless medium. If u have been going online wirelessly [ wi-fi ] at your home then u should not be having any problem going online wi-fi outside your home. All u have to do is [ at the resort ] associate to the available wi-fi network and enter password [ if any ] and u will get connected.
But if u have been going online via wired medium and never wi-fi at your home then u need to go for a external wi-fi card [ basically a PCMCIA card ] or a wireless USB adapter for your laptop.