My nephew is gonna be on the radio tonight. I'd like to record the stream either from iTunes or from my web browser.
What are my options to accomplish that?
VLC has an option for listening to network streams, so if VLC is compatible with the stream that you want to listen to it also offers an option for saving that stream to your HD. In the dialog box that lets you enter the stream URL there is a drop down menu by the OPEN button that lets you save the stream.
Of course this does depend on if VLC will open the specific stream you want it to. Many streaming services use special players and DRM to prevent such things. Failing the VLC method Tetsujin has an excellent recommendation in Audio Hijack as it doesn't care about any of that and just records all the audio passing through your Mac.
I'm not aware of any recording feature in iTunes for Internet radios. Check if the specific radio station has a webpage/webstream and you might be able to record that via your standard audio recorder in the OS of your choice.
If you have access to an iOS device, the app Audials has a recording option and it's free of charge.