Check your tire pressure. The shops never fill it properly when balancing. If the balancing really is good, then try an alignment. If the alignment doesn't take care of it then it's most likely a worn control arm bushing, worn ball joint, worn tie rod end, bent suspension part, worn wheel bearing, bad shock and/or spring or worn steering rack mount bushings.
That should narrow it down a little.
Be patient, these things can really be a PITA to find if it's a worn part.