Audio-Technica M40X are great for the price, from my experience.
I haven't personally used them, but I've seen the Philips SHP9500S get recommended often for ~50-60$ on sale, and they're on sale pretty much all the time. They're open back and have a detachable cable.
Here are some other suggestions near and under 100$ from r/headphones:
https://sites.google.com/view/headphoneadvice/closed-back-headphones/category-100 (closed back)
https://sites.google.com/view/headphoneadvice/open-back-headphones/category-100 (open back)