Stand along side the bike and firmly apply the front brake. Then try to rock the bike forward and back. If you feel any movement in the steerer tube the head set needs to be serviced. Your LBS can do this for you. If your bike is fairly new it most likely just needs to 'tightened up'. The techniques for this depend on the type of headset, threadless being the most common on more expensive bikes. Check Google for videos on this. If the bike is older, the headset bearings may need grease or even replacement. Neither is complicated and can be done in your home shop. Your LBS would be happy to help as well.
If there's no movement when your rock the bike back and forth, I'd suspect that the clamp securing the handle bar is loose. Tighten all the screws. It's best to use a torque wrench for this.
Tracking down noises can be frustrating. Keep at it.
Good luck.