Try PCPartPicker's search tools. Here, for example, are the results for cases with at least 3 internal 3.5" bays, 3 external 5.25" bays and front-panel USB3, priced under $120...
https://pcpartpicker.com/products/case/#G=3,12&J=3,20&X=0,12000&D=4,2
Unfortunately, they don't let you specify the number of front-panel USB ports, but that should help narrow down your options a bit. It might also be worth simply getting a USB3 hub, and keeping that on your desk, connected to a port on the rear of the system.
Edit: That Phanteks Enthoo Pro Tempered Glass actually looks pretty nice and modern though it's at the top of your budget range. Actually, it seems to be the only option with a tempered glass side panel that fits those criteria, if seeing your compenents is something you are interested in. It also appears to have two USB2 and two USB3 ports behind a panel at the top, along with headset connectivity...
https://pcpartpicker.com/product/Tb...l-edition-atx-full-tower-case-ph-es614ptg_swt
Most of the recent cases with tempered glass have tended to do away with external drive bays entirely, so you're probably not going to find many cases with lots of them. Cutting the optical drive bays down to two or one might open your options up a bit more though.