My brother-in-law restores old cars, and he has quite a stock of products on hand to make those vehicles look as good as possible. He uses Prime Power Brand Prime-Shine Auto Glass Cleaner to do the glass, mirrors and chromework on his vehicles. It seems to do a good job.
This glass cleaner leaves a streak-free shine and is ammonia-free. It is also safe for tinted windows.
You must be careful not to get any of this product in your eyes, and it should be kept out of the reach of children because it is harmful if swallowed.
Just spray on the surface that needs cleaning and wipe with a dry cloth or paper towel. I would use a cloth because paper towels can sometimes scratch. This product can also be used on tile and porcelain, but it is not to be used on wood surfaces.
I tried a little bit of it in the bathroom on the mirrors. It really did a nice job with no streaks. And the spray is powerful, one or two sprays is all you need to do the area that you are cleaning.
This product can be purchased at any auto supply store, though I don't know the price because my brother-in-law usually purchases it for his vehicles. The bottle he has is 32 fl oz, which should do a good bit of work.