Using a wireless-to-wireless router in your room does not add any real security. Although the wireless network it creates may be "secure", the hotel wireless network it connects to is not. All internet traffic is still exposed to snooping. And wired connections are not secure, either. Anybody else plugged into the same hotel network can use a packet sniffer and see all of your traffic. This isn't quite as terrible as it sounds, because most reputable banks and such use "https" so that credit card info and passwords are sent in an encrypted format. But https isn't bulletproof and there's a good chance you sometimes sent that info to websites without encryption.

The only realistic way to create real security it to use good VPN software such as OpenVPN. The standard Microsoft VPN software (PPTP) is known to be insecure. OpenVPN is available for ipad, iphone, android, Windows, etc.

To use VPN, you need to either setup your home router to accept VPN connections if it supports it (which is what I do), or purchase a subscription to a VPN service.