The Warden's office is in the Administration area. Just enter the building and keep going right. When you reach the room where Joker set off the bomb in the cutscene, keep going right and you should reach a very long room. Use your Line Launcher to get across.
If worst comes to worst, go to the map and press triangle. That should show you where your next objective is. --- Persona 4 Golden has taught me that I need to focus on maxing my S.Link's IRL. PSN: ChaosxPaladin
By "Warden's office" do you mean trying to free the Warden, or are you tracking the Joker? --- *Insults hold no weight with me. Well thought out responses hold my respect. Integrity is amazing, so use it.*
The ! on the map moved. Go back to the entrance and it'll point you to the right. I could tell you more after that, like you'll basically be sneaking in from the roof, but I'm sure you'll get it once you're on the path.