You will be fine driving without swaybars.. I would disconnect the broke pieces and tie your sway bar up so it doesnt get in the way of steering components. Fill out your jeepforum profile with info on your rig. If you have a lift you will need extended sway bar links. If not, you can just find some stock ones on the internet.
Just remember your Jeep isnt a sports car and you are fine. I have my front sway bar completely removed on my TJ with 4" lift. I just leave the rear in and call it a day.
97 TJ Dana 30 w/ARB Solid Cover, Currie 4" lift, Ford 8.8 w/ Riddler Cover, Currie Steering, Trail Gear Front Bumper, LOD Rear Tire Carrier, Smittybuilt XRC8, 35" KM2's, 5100 Bilsteins, Teraflex Oil Pan Skid, Poison Spider Sliders, Rock Lights etc.