I bet that it's the bearing or axle issue. Wobbly wheel is when you do not spin it, but move it from side to side and it moves quite a bit - right? That means the axle could be broken, or bearings shot, or nuts on the axle that seat the bearing are not adjusted properly and the bearing move about on the cones.
http://www.sheldonbrown.com/gloss_an-z.html#axle