Yesterday, a strange thing happened: I landed at a towered airport and when I got on the runway both myself and my CFI swore the ground guy said exit on taxiway A - which we did. Problem: There was another bird coming towards us on the same taxiway. Eventually, ground said we exited on the wrong taxi and after turning around and moving over everything went smoothly. Outside of me looking like a student pilot (which I am btw) nothing actually bad happened. Ok. So two questions: 1) Are there designated exit taxiways off a runway? I didn't think so, and I thought I had the option to exit any taxiway that isn't taken or obstructed off the active before I cross the hold short line and call ground. 2) Can I choose a different taxiway then what the tower tells me? The reason why I ask is I might not want to step on the brakes or pull back on the yoke so hard just to make a taxiway. I rather pick one I feel comfortable with after I have dissipated enough energy on the ground. I read the FAR/AIM and I didn't see much regarding this other than listen to ATC when instructed to. But what are my options getting off a runway in a towered airport?