This is From the Mixed-Up Files of Mrs. Basil E. Frankweiler, by E. L. Konigsburg.
The brother and sister in question are Jamie and Claudia Kincaid, who run away from home. They live in the Metropolitan Museum.
Jamie did both of the things that you describe with the cards:
Jamie wanted to sit with his buddy, Bruce. They played cards on the
bus; each day meant a continuation of the day before. (The game was
nothing very complicated, Saxonberg. Nothing terribly refined. They played war, [...]
Every night when Bruce got off at his stop, he'd take his stack of cards home with him. Jamie would do the same. They always took a vow not to shuffle. At the stop before Bruce's house, they would stop playing, wrap a rubber band around each pile, hold the stack under each other's chin and spit on each other's deck saying, "Thou shalt not shuffle." Then each tapped his deck and put it in his pocket.
And about the PO box:
"Here's the plan: we rent a post office box in Grand Central. Like when
you send in box tops, you always send them to P.O. Box Number So-and-so.
We write a letter and tell them to answer us at the box number. After they tell us that they need help, we reveal ourselves. As heroes."
And the quarterly part:
"For how long?" the man inquired.
"For about two days."
"Sorry," the man said, "we rent them quarterly."
"All right, then. I'll take eight quarterlies. That makes two days."
"Quarter of a year," the man said. "That makes three months."
Regarding the bed:
At last she found a bed that she considered perfectly wonderful, and
she told Jamie that they would spend the night there. The bed had a tall
canopy, supported by an ornately carved headboard at one end and by two
gigantic posts at the other.
Lastly, you also noted about laundromats in the comments. They are mentioned 4 times, here's one:
They packed their gray-looking laundry back into their pockets and
walked to the door of the laundromat. At the door Claudia turned to Jamie
and asked, "Can we ...?"