Miki's super-costume will be shown on the dressmaker's dummy (unless she's wearing it).
Click the wardrobe to browse Miki's outfit collection. Select her civilian and heroic outfits here.
The white patch on the wall will be the city map, which will accumulate sticky notes and bits of red string as the game progresses. Clicking the map takes you to a quick-travel screen, to send Miki off on a mission.
Click the bed if you want Miki to take a night (or day!) off.
Click the crime computer (laptop) to pick up news, hack the police, or review quest notes.
I love the idea of trophies, so expect the lair to develop more clutter with each quest completed.