We aren't really sure it's a mansion; we just liked the alliteration.
Actually, we aren't really sure where any of this story takes place. With some notable exceptions, Seuss has never been one to put a lot of detail into his settings. Remember the Sneetches? They lived on the beaches, and even in the illustrations, we got nothing more out of Seuss. No sense of topography or longitude and latitude. Nothing. But we here at Shmoop say that's peachy. This isn't objective realism here, folks. It's got another goal in mind.
So, why the minimalist approach to the setting? Good question, and it's one we imagine has many possible answers. Here are two. Feel free to come up with your own.
(1) Keeping it vague keeps it universal. The lack of detail in the who, what, where, when, and why of Marvin K. Mooney gives the reader a chance to fill in the blanks for herself. Like a thematic Mad Libs, it produces a story and reading personalized for the reader, by the reader.
The same approach works for the setting. What are those green things the Narrator is hiding behind? Doors? Columns? Walls? Are they even architecture? Where is Marvin K. Mooney supposed to go? All fine questions, dear reader, and these questions provide the setting with what's called universality. In other words, it could take place anywhere at any time. If you need something a little more concrete than that, you can have it, but you'll have to answer the questions yourself. The story won't be doing it for you.
(2) The minimalist setting helps keep distractions to, well, a minimum. Seuss wants children to pay attention to the language of his stories. The rhythm shows how fun language can be, and the repetition of words in different language functions can help children grasp the nuances of reading.
If Seuss packed his backgrounds like a hoarder's closet, there would be too much mess and clutter for the children to properly focus. Instead, he uses a minimalist approach, giving the words their proper place on the page.
So, there are your two possibilities, as promised. Can you think of any more?