I have been able to find quite a few radio channels to add to Rhythmbox using the advice above and this is how I do it, but it is based on UK radio and using Firefox:
Go to the radio station in question, such as classicfm
Click on the "Listen" button (in this case top right). This brings up a new window (and usually an advert you have to endure). Then right click somewhere in blank space and select "View Page Info". Switch to the "Media" tab and look for the Address with the Audio Type, right click and Copy. In this case it's http://media-the.musicradio.com/ClassicFM
Go into Rhythmbox, click Radio and then Add.
The link should be automatically pasted in from the clipboard and click Add.
The station will now be in the list, but displayed as the weblink.
Double click on the link and it will automatically assign the station name and you're done!
Update
By using radiomap.eu and navigating to your location and city, I've found it a lot easier to strip out the Audio link.