Answer: SNAPES CLOSET

The puzzle answers are:

Since the sets of initial and final letters are identical, there is a natural cyclic ordering of the answers. The long cyclic string you get from concatenating them (EATENOSESEASALTINCUPULSARIPOSTE...) makes a Hamiltonian cycle on the Marauder's Map, where each initial letter of an answer goes in the space corresponding to that puzzle. There is always a unique shortest path between two consecutive puzzle vertices, and this is always the right place to put the letters.

Once all the letters are written in, the middle rows of the map spell out SNAPE’S CLOSET.