Is there a best aperture to shoot with on each lens?

For each lens is there a specific aperture that produces the best image quality? Why?

How do you find the best aperture and what would it be on my Nikkor 18-200mm 3.5-5.6?

Usually the sharpest aperture is either going to be near the middle or at the closed end of the aperture.

Usually it's a couple of stops down from wide open. Lenses wide open tend to exhibit softness & lenses full stopped down show diffraction.

All lenses do have a "sweet spot"

Finding it is entirely random. Usually, it's in the half open to maximum aperture area. A result of mass production by humans is no two things are exactly the same. It's up to you. Take lots and LOTS of pictures and take note as to which one is at which aperture. Study these images. Look at them at 200% or higher. You'll find your sweet spot.

Even that "sweet spot" mentioned is somewhat arbitrary. It depends on what the photographer wants from the image. A smaller aperture, makes for a tighter depth of field. A larger opening allows for a good exposure at faster shutter speeds. That's why a choice of settings is preferable to having only one.

Diffraction and interference are degrading factors. Light rays as they just brush by the blades of the aperture stop bring on diffraction and interference that degrades the optical image. Thus as you stop down the resolving power of the lens decreases. This phenomenon is called the Rayleigh Criterion.

Other factors are afoot to degrade image quality. These are called aberrations and they are present in every lens. These are induced by unavoidable errors in the curve shape of the lens and the density of the material of construction. Aberrations diminish greatly as the lens is stopped down.

These degrading influences comingle. As a rule-of-thumb, the best aperture setting that delivers the highest resolving power and acuity will be two aperture stops down from the largest opening.