The steering dampener nor any other part in the front end can CAUSE a vibration. Bad parts can allow a vibration to be exacerbated, but only ROTATING parts can CAUSE vibrations.

The most common cause of vibrations are indeed tire related. Of the tire related causes, the most common cause is when the tire store kids do a static balance rather than a dynamic balance. A static balance involves putting a weight on the inside lip of the wheel only. This will prevent the wheel from hopping up and down, but on todays nimble suspensions this is not good enough.

A dynamic balance uses wheel weights on the inner and outer plane of the wheel and prevents the wheel from wobbling. The tire store kids avoid this because they get yelled at when they scratch alloy wheels with wheel weights. To dynamic balance WITHOUT scratching alloy wheels, a savvy wheel balancing tech will use tape weights just behind the spokes of the wheel for the balance of the outer plane.

If your tire store gives you a blank stare when you tell them that you want your wheels balanced this way, find another tire store.

As far as steering dampeners and other front end parts, I would not replace them until I got the vibration to go away. That way you have a system that will more easily tell you when a wheel is out of balance. Once the wheels are properly balanced then, of course, find and repair any loose or worn front end parts.

Good luck,