I believe it's at "The Hollywood Museum," or at least it was at one point
Not anymore. I was there a few weeks ago, but the museum certainly has exhibition space large enough to see how they once fitted it in!
Currently, they have on display, in a science fiction section: Kirk and Spock's fatigues from ST V, Scotty's engineering suit from the movies and Data's Season One/Two uniform from TNG (modified with the Season Three collar, for an extra to wear).
The bridge was rebuilt from the ground up for TFF because it had been modified to death for TNG. Herman Zimmerman designed an entirely new bridge, only the Turbolift alcoves remained from the previous TMP-TVH set.
Not quite "the ground up", because when the sets were finally dismantled after "Voyager", to clear the decks for "Enterprise" sets to go in, there were still
wooden support struts, now rotting very badly, marked for their use in the bridge originally created for "Phase II" in 1977.