"Internet Radio" gone from iTunes 12.7
The traditional "Internet Radio" feature is not gone from iTunes 12.7.
The feature for offering free for all internet radio streams was not removed from the application but may be hidden and is now named competitively with another "Radio" feature within iTunes.

Check Restrictions for Traditional "Internet Radio"

It may be invisible to you because you may have a setting active in  

 iTunes &gt; Preferences &gt; Restrictions &gt; Internet Radio


Obviously, the checkbox under Disable: Internet Radio needs to be off.

Re-Add Traditional "Internet Radio" to the Sidebar

More likely is that the new default preferences violate again Apple's own Human Interface Guidelines:

The first "Library Sidebar" for "Music" in its default state is simplified: without Internet Radio visible. And you do not see how to customise it until you hit an invisible spot to the right of the sidebar section title called "Library" when your sidebar is set to display "Music". Hovering to the right over an apparently empty spot then reveals an "Edit" option where you can then activate the "Internet Radio" setting. Click "Done" if you are done with your customisations in the same spot to re-hide that user-confuser and traditional "Internet Radio" will be in your sidebar again.



That gives you the old big list with a tree structure to choose from.



Adding Custom URLs for Traditional "Internet Radio" Streams

Opening a custom stream is accomplished by entering the URL in the box that appears when pressing Command+u or choosing the menu item File > Open Stream.

Adding this permanently seems not possible.
But again: right-clicking into the info area (The Apple logo in the picture) reveals the option to "Create Station".

Interestingly you can also create playlists with those streams to get them organised to your liking.



The new "Apple Music"-"iTunes Store"-"Radio"

An alternative to this method of interfacing to streams is a much more prominent store-like interface for radio stations that looks like it is somehow tied to Apple Music (this one requires from you to give up at least your AppleID or even subscribe to the "Apple Music" service):


Possible restrictions for that are in iTunes Preferences as a subset under "iTunes Store" and a part of "Apple Music".