I second the Audio-Technicas. My headphones are the ATH-M50x, I've used them almost every singe day for almost a decade, and they're still going strong. I've had to replace the cord twice, the ear pads twice, and I put a cover over the top once the fake leather started falling apart ~5 years in. The sound is still good, they're still comfortable, and they show no signs of falling apart or anything, even though they get dropped on the floor at least once a week lol.

Apparently they have the M50xBT2 now, which is a bluetooth version, for $200. If the quality is the same as the wired version, I'd say it's worth it, but that does put it $50 over budget.