Sony MDR7506 Professional Headphones
There's a reason you always see this headphone in studios around the heads of everyone from recording engineers to radio talk show hosts–it makes accurate sound and isolates noise. They have excellent isolation, keeping outside noise out and keeping the sound in.
They're half the price of Beats and sound ridiculously better. (Why anyone would buy Beats is beyond me, but hearing is believing.)
They do fold, although not very compactly. I keep mine in the house.