In the sentence below, there are all kinds of names for what nice is.
But the sentence above has been done things to. An equivalent sentence is
from which the first sentence is derived by To-be-Deletion.
In other words, there is an infinitive complement here.
And (be) nice is its predicate adjective.
What you want to call nice after to be is deleted is up to you.
I won't go into A-Raising here, but seem is a prototypic A-Raising verb,
since what actually seems in this sentence is in fact not her, and not nice, but rather
that she is nice.
That she is nice is also a possible complement clause with seem, although it requires Extraposition.
- It seems that/like she is nice.
And it means the same as the other sentences.