I've had a pair of Shure SRH-240s and they don't focus on "dat bass", they do lack a fat low end, but these make any bass guitar so clear sounding in any sort of music anyway. Since the mid range and higher is more important in all music, these headphones have that boosted warmth and the clarity in the high range is superb. I haven't heard anything like these whilst keeping the budget just under $100. They're closed backed considering closed back is always > open air (at least if you're a serious fan of music).
But anyway, that's just something for you to think about. Don't get a pair of headphones that have an enormous low end that it makes any sort of music sound like the mids are scooped out. The Shures have a very even EQ spectrum.
For a budget of $100, you gotta look around the place a lot. Test lots of types of cans and in the end it's all about what feels good on your head and what your favourite kinds of music sounds like through them.