Can iPad be used without internet

Yes you can providing that you get it activated 'in store' which they will do for you.

Downsides are that you will have no backup until your computer is up and running at home and the device synced to that.

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Aside from needing an internet connection and iTunes to activate the device initially, it can be used without internet connection for all things that don't require on-line access, such as Maps, iTunes and app stores, Safari, Mail, etc.

You can sync it, yes, but you can't activate it that way because for the activation, iTunes needs an internet connection.

However, it can be someone else's internet connection with a suitable copy of iTunes and compatible system - it's possible that the store might be able to do this for you (though Best Buy likely can't).

If you are planning to take your Mac mini there, then make sure you have a compatible version of MacOS (10.5.8 or later) and iTunes (v9.1). That way you can also download and sync the first round of apps you might want (I went mad and grabbed 20 odd) because that doesn't take long and you'll probably want to add some apps!

After that, back home with no internet you can continue to sync any other data such as calendar and address book, music etc without needing the internet.