You asked: "Where is far enough away from Boston and where exactly is the official city of the Cat in the Hat"
Theodor (Ted) Seuss Geisel was born in Springfield, Massachusetts (They wanted the Simpsons to live here too, but I guess it was too crowded for them). in what was once a very nice neighborhood. I don't know if his house still stands but I remember seeing it growing up. Springfield is approximately 100 miles due west of Boston. It sits on the Connecticut border. During Geisel's time it was referred to as the City of Homes.
There is a large display dedicated to Seuss's characters at the main branch of the Springfield Library at State and Maple street....not far from where he grew up.
For quick trivia, Springfield is also the home of the Basketball Hall of Fame and the Titanic Historical Society Museum.
Thanks for the welcome....sorry it's not the official welcome thread.