Block device from accessing the Internet, but not Wi-Fi
To prevent a device from accessing the internet, but allowing it to access files on a local network over Wi-Fi you can setup an ad hoc network.

The ad hoc network will be hosted by your Mac and devices, like your Eye-Fi card* or your kids laptop, can connect to it and access shared local folders.


Turn Airport On


Click on Create a Network. The following screen will appear:

If you want password protection, check Require Password and type a desired password.

Hit Ok. Now you're Mac is broadcasting a network.


The Eye-Fi support page explains how to connect to an ad hoc network.


Note on the Eye-Fi card: according to this website only the Eye-Fi Pro and Eye-Fi Pro X2 can connect to an ad hoc network.


General note: if you want other devices to access files and folders on your Mac those files and folders have to be shared. How to do that is suitable for another question.