Merton can't stand his hotel in Venice because it's full of a bunch of annoying tourists and no authentic Italians. First world problems, guys. As he sits around postponing his visit to Milly, he gets angrier and angrier about the way Kate manipulates him into doing whatever she wants. He begins to wonder if he has any will of his own any longer. Hate to break it to you, Mert, but the answer is probably no.
He decides that before he goes any farther with the plans, he needs to prove to himself that he still has some cojones left. We're not sure yet, though, how he plans on doing this.
He leaves his hotel and rents some old rooms. The narrator makes it clear that (at this point, anyway) he definitely hasn't rented these rooms for the sake of seeing Milly Theale.
He finds himself resenting and disliking Milly more and more. He also thinks about leaving Venice immediately. But he realizes that the only thing he can still do that's helpful and good is to avoid being a jerk. Especially towards Milly.
Nonetheless, his resentment toward Milly (and Kate!) continues to grow the longer he's alone in his rented rooms.