IOS – Updating iOS through public WiFi in hotel

Fortunately for you, iOS will not update without your consent. You have to physically go in and choose to Download, and Install the Update (two steps) in order for it to update to the next version of iOS.

iOS 5 or higher have a feature called OTA (Over the Air) updates, which bring the convenience of not having to plug your iPhone into iTunes to update it - which you are aware of. It displays a badge on the Settings app on iPhone homescreen, but this will still not update without your consent (unlike some Windows OS updates).

Unfortunately, the Settings.app is not in the list of notifications that you have control. So you will have to get used to seeing the "1" on the Settings.app.

You will also have to be careful to decline (skip) updating your device anytime you plug it in via USB to iTunes. One thing to note, is that you don't have to worry about Wifi syncing with your device. It will not update your device using iTunes Wifi sync.

There's a good chance the WiFi you connect to actually might not have a working internet connection but is still broadcasting a WiFi signal. I suggest you to try and connect another device and see if the same helps.

Also, as the comment above suggests you may need to log into the network for the same to allow you to use the internet. To login, you should see a login screen right after joining the network or try opening any website from Safari, that will make the login screen show up too.