Room recess
(Other definitions for nook that I've seen before include "Interior angle formed where two walls meet" , "small secure zone" , "Secluded corner" , "Alcove" , "Cubbyhole" .)
'room recess' is the definition.
(I've seen this in another clue)
This is all the clue.
(Other definitions for alcove that I've seen before include "sheltered spot" , "nook" , "private part?" , "Recessed area" , "compartment" .)