How can I tell what kind of iPod Touch I have if the case can't be removed?
Plug the device into any computer with either iTunes or the iPhone configuration utility and it will tell you the model, serial number and much more about the device. Both software packages run on Mac and Windows and are a free download from Apple.

An alternate method of determining whether the Phillips Hue app will run is to have them download that app since the App store includes built in checks to ensure the device meets the app's minimum requirements. I could see how this might not be ideal if part of the gift is to be a surprise that downloading the app might spoil.