I would put "in" instead of the "of" so the first room in the hall. At least if you are specifying a direction, along with either right or left in less the rooms are staggered or only one side.

Do you mean "off the hall"? In other words, you reach the room by going through the first door in the hall on the right or left? If you could explain your situation more, then we can try again.

I would rather say " The first room across the hall "