First thing to check is the steering column bushing. It's made out of nylon, and over the years tends to disintegrate. To check the bushing, sit in the driver's seat, grab the wheel, and move it up and down and side to side. If you have play, then the bushing is bad. Our host sells a metal sleeve to solve the problem. It's about $15, and takes an hour or less to install. Here's a
tech article on replacing the bushing.
If your problem isn't the bushing, then you should probably take your car in to a reputable tire shop and have them check the balance on your front tires.
I'm sure others will chime in with suggestions, but these areas are where I would start my inquiry.
Good luck.