Word for something that is modified
Solution 1:
There might be a specific linguistic term. But I don't know it, and I wouldn't be surprised if there isn't one.
So how about subject? Or if that's got too many connotations for the context, perhaps target?
LATER - I'm also minded to wonder why there might not be an established term. Adjectives and adverbs are easily-identified 'modifiers', but actually a modifier can be a pretty long subordinate clause in a sentence. And the text element(s) it modifies can be complex too.
The lack of a term might simply be down to the conceptual difficulty of naming something so epen-ended. It might just be the noun next to the modifying adjective, or it might be the whole sentence excluding the modifier. All they have in common is the capacity to be modified - not a very significant attribute for most considerations.
At least with actual modifiers, you could say their capacity to modify is a defining characteristic, so it makes some sense to identify and name such a linguistic class. The things which they modify are so heterogeneous it's a bitmeaningless to lump them all together as a class with a specific name.
Cutting to the chase, I realised that the obvious candidate would be modificand if I really needed such a word, and Lo! - it turns out linguists do indeed use that term when pressed.
Solution 2:
There is in fact a generally accepted word: head.
Fat John is a noun phrase and John its head.
Eat slowly is sometimes considered a verb phrase, and eat would be its head.
Computer-related is a compound adjective / adjective phrase, and related is its head.
The head of a phrase is its core, the part that determines how the phrase as a whole behaves. As you can see, the head of a noun phrase must be a word that functions as a noun, etc.