I'd put a fermentation chamber in the alcove if it's large enough. I built a 38DD and put it in our living room because my closet is too small for it. However, my brew kettle, and cases of bottled beer reside in the bottom of that closet. My empty buckets, bottle tree, hoses, etc etc reside in the mud room.
With a little organization, you could ferment in there, store your bottles in there, store your kettle/buckets/carboys, etc etc. Kind of a "one stop shop" for everything brew-related. Whenever it's time to brew, just go grab whatever you need from the closet.
Brewing Since July 2012 All-grain BIAB
Primary 1: Raging Irish Red
Primary 2: Lilsparky's Nut Brown Ale
Secondary 1: Skeeter Pee
Secondary 2: Air
Kegged: Two Hearted Clone, Graff, BM Centennial Blonde (again :) )