The Stateroom is Admiral Merlwyb's private chambers in Limsa Lominsa, so it's a special area not usually available to the player. You're on the envoy quest right? The quest should direct you to a roegadyn npc in a red coat in front of a lift that you cannot enter in the entrance area of Limsa Lominsa's lower decks (the 'Bulwark Hall'). Speak to this person and if you're on this quest he'll ask you for identification, in which case, hand over the letter your head of state gave you to access it. You'll then enter it automatically.

Hopefully this has helped.

EDIT: Aeika beat me to it, phooey.