Can you tell if the noise is front or rear or left or right side. I have seen the outer sway bar links (made of black plastic) break in the front of the car at either side and I have seen the rear sway bar itself break. Its hard to guess without hearing the noise first hand.
It could be many things, the exhaust and exhaust heat shields also give problems causing a rattle usually worse when cold or at a certain engine RPM.
My 2000 Outback had similar situation. Rattle at slow speeds, tracked straight but steering had a funny shimmy. I replaced the struts, motor mounts. Different shop said ball joints. . . bingo. Inexpensive fix, big positive result.