If you were ever confused about where Frasier's study was, well... you're not alone...

The room with the ? mark is thought to be Frasiers study, mentioned in season 1 episode 1 the convo about hiring Daphne:

Frasier: Dad, I'm not having another person living in this house!
Martin: Give me one good reason why not!
Frasier: Well, for one thing, there's no room for her!
Martin: What about that room right across the hall from mine?
Frasier: My study? You expect me to give up my study - the place
where I read, where I do my most profound thinking?
Martin: Ah, use the can like the rest of the world!

Season One Episode Two: Space Quest:

Frasier: Daphne? What are my things doing here? My leather wing chair?
My Kusami lamp?
Daphne: [entering from back where her room is, carrying a box] We're
putting them in the storage room, in the basement. There was no
room for them in the study once we got my furniture in. We
discussed it last night, remember?

Season One Episode Ten: "Oops"

Bulldog's girlfriend kicks him out after he gets fired at KACL, so he asks to spend the night at Frasier's...

Bulldog: Thanks, Doc. Hey, I hope it's okay, but I could really use a
hot shower.
Frasier: Oh sure, sure.
Daphne: Down the hall, second door on the left. Towels are in the
cabinet.
[Bulldog heads for the hallway to where Frasier's room is]

Thus, the mystery room is a bathroom!

This picture is a blue print pic I found on the Internet and restored (cleaned it up and tried to type in as much original text as possible.) The text outside of the apartment is what I fabricated.

Come Lie With Me: The ep where Daphne wakes up with Joe in her bed and tries to hide it from Frasier. Here's a conversation they had a day later in her bedroom:

Frasier: That is not what I meant. This is difficult for both of us,
Daphne. I have to express my feelings. I also don't want to
lose you. You're very important to me and my father.
Daphne: That's why my solution is best. I'll still be here during
the day to take care of your father but nights and weekends
I'll just go home to my own place. On top of which you can
turn this room back into your beautiful study you used to
have.
Frasier: Well, I suppose, what other choice do we have?
Daphne: Of course it'll be a period of adjustment for all of us...

(Whilst she is talking Frasier begins to look round the room and a
smile starts to form on his face.)

Daphne: ...I know how much you two care about me and consider me part
of the family but... [notices Frasier's smiling face] You're
picturing your study right now, aren't you?
Frasier: [sheepishly] Well, you made me!

and one I enlarged x2

Notice how Martin's chair isn't the same one used for the show and the paintings near the fire place were changed before filming the show.

No Baby Grand Piano yet.