I've found that wanting a headphone for gaming and for being mobile is tough to balance.
Generally open headphones work far better for gaming, at least in my experience. The sound stage and open sense you get really helps for immersion in video games. Open headphones for mobile purposes just don't work at all because of the sound leaking in/out, so automatically it's a big problem.
I personally can't use anything on ear when outside, especially when it's warm. A better option would be to grab a $200 pair of headphones for gaming (maybe cheaper), and a nice set of in ears for being out and about (you can get a decent set for $50)
I use a set of HiFiMAN HE400's at home with a Schiit Magni and Modi amp/dac for music and gaming, and I use a set of Audeo 012 in ears for being out and about. This is significantly over your budget, but you get the idea.
MLE has a great guide on selection of gaming headphones for many price ranges here:
http://www.head-fi.org/t/534479/mad-lust-envys-headphone-gaming-guide-update-7-9-2014-ultrasone-hfi-15g-added
edit: Reading your post again made me realize maybe you just mean mobile as in moving around your home and not out doors
either way, the reviews from MLE on the gaming side of things might help you out!