Bad strut. Worse and only case I know of.... Cousin was driving at around 60 Mph and the front passenger tire started wobbling. Any speed over 40 Mph the tire would wobble. He drove another 30 miles like that. Under 43 Mph or so the car drove fine.

The piston inside the strut snapped and because his tire wasn't balenced it wobbled. This was a heavy car compared to yours... 1998 88 oldsmobile.
He was told the wheel bearing was bad and when he bought the car in for inspection the vibration and tire movent was blamed on the wheel bearing...

 

I too bought a 2000 neon and it had very similar problems.
An alignment should cost u about $55. The lower engine mount is $40 at autozone and takes less than half an hour to replace. I didn't do the tie rods but they are fairly cheap too. The rear struts (ready mount) are $160 each at autozone, and can be done in under an hour. None of this is overy complicated and can be completed with a basic set of tools