Dear Cacher,
Welcome to The Ersatz Elevator. I am sorry you have stumbled upon this unfortunate series of geocaches, a word which here means tupperware hidden in the woods located by using multi-million dollar satellites. If your luck is better than that of the Baudelaire orphans, you can solve the puzzle below to find the coordinates of this cache before Count Olaf does. DO NOT GO TO THE POSTED COORDINATES and, please, use HIGH STEALTH so you and the cache are not apprehended by the authorities or by muggles, as Lemony Snicket has been. In fact, you may want to seriously consider using the dark abyss of the night for your cover.
Violet Baudelaire walked into the lobby on the ground floor, just under the first floor, of 667 Dark Avenue, where her new guardians lived in the penthouse. She was already exhausted as she eyed the spiral stairwell she had to take to the apartment, as her guardian, Esmé Squalor, had had the elevator removed. She began trudging, but when she reached the forty-first floor, she realized she had lost her hair ribbon somewhere in the lobby, and returned to the ground floor. Once the red ribbon was secured in her hair so she could think of a new invention during her climb, she began her journey up the stairs once more. On the ninth floor, she happened upon her brother Klaus, who had been visiting a neighbor with a grand library. He informed her that their little sister Sunny was receiving cooking lessons on the fifteenth floor and that they needed to retrieve her. After their slow climb, Violet picked her little sister up in her arms, but bumped into Klaus, whose books tumbled down the spiral staircase to the tenth floor.
The Baudelaire orphans chased the books down the stairs to find that their guardian, Jerome Squalor had caught the tumbling books. He excitedly told the children about a new bistro in the restaurant district that he wanted to take them to, but informed them that they first had to run a few errands around the apartment building for his wife Esmé. They first descended to the second floor to pick up Esmé's pin-striped suits which she had dry cleaned, then climbed up to the thirty-fifth floor to retrieve the latest list of things that are "in". After stopping back on the twenty-seventh floor to check on final details for the "In" auction, the four continued their way up to the penthouse so that Jerome could retrieve his wallet. Upon reaching the thirty-sixth floor, however, they ran into a disguised Count Olaf. In an attempt to escape from his clutches, the children bolted up to the forty-fifth floor and backed into an alcove until they saw Olaf run past them up the stairs. After a moment of scared silence, they quietly made their way to an abandoned apartment on the forty-second floor and have been hiding out there since.
You do not have to have read Lemony Snicket's very forlorn diatribes in order to solve this puzzle. Check your answers below and proceed at your own risk. Please do bring your own writing utensil.
With all due respect,

P.S. This cache is #6 in A Series of Unfortunate Caches. In order to solve #13, you need to take careful note of the letter / number combination hidden inside each of the physical caches #1 through #12.
P.P.S. Congratulations (or perhaps apologies) to styx for FTF.