Audio Technica M50s fit your request. They are balanced (just that perfect amount of bass thump), closed, stylish , and very durable, although because of this they're a bit bulkier than most portable headphones. I personally feel comfortable bringing them anywhere, driving them with a Fiio E5 using Line Out form a Classic and just love the sound.
They can be had for less than 120 USD nowadays.
Ooh, that was quick. Thanks.
Reading reviews, they look really nice. I'm just worried about one thing: It says the impedance is 38 Ω, while my player says it's output supports only 16 Ω.
I don't really know what that means, though. I'll look it up, but is this something i should worry about?