Best gaming headset without mic for under 100$

Pretty much all gaming headsets come with a mic bundled in. You could look into the Beyerdynamic Custom One Pro but it's over your budget. I could suggest that you look into the older models like the Thermaltake Level 10M Headset or the Kingston HyperX Cloud(I).

On another note, how do you plan to connect the headset to your system? If you're looking at a mixer then might as well go for audiophile grade headphones.