Hi, Matching Mole.You must use a prep. such as over or onto. Usually "over" if the room is on a higher floor, "onto" if the view is at the same level. The garden is outside the room.
"To look out" + noun without using a preposition is informal for to select, or find. "Will you look out those plans for me" (get them out of the file).
So your 2. example is fine. It describes the fact that the room overlooks a garden attached to the building it is in, and is probably on an upper floor.
I feel this must be AE because it doesn't sound right to me, and I don't think I would use it. I can see it used on UK sites, but it doesn't seem that common. Many of these are "looks out to sea", which is something of a special case, but even then, I think I might only use even that with an animate subject."To" will work too.
"The hotel room looked out to a beautiful garden."
My back yard looks out to my swimming pool.
My front window looks out to sunrises; my rear window looks out to sunsets.
These sound OK to me.
Although it's not a construction I would use, I certainly do find a lot of examples of it on the internet:
It may just be a personal preference on my part. It's obvious that it's used by many people.