If you find rust on your stainless steel items you can use lighter fluid to get rid of the rust fast.
Rubbing the rusted area with a bit of rubbing alcohol will remove those hard water stains that you hate as well.
If you have hard water stains on your stainless steel fixtures you can remove them with kerosene. Kerosene does have an odor but this will go away in just a few minutes when you let it air dry!
For a particular tough stain you can rub the stained area with a crumbled ball of aluminum foil. The aluminum foil is going to rub the metal surface so be careful not to do it too often or you could rub away all the plating on the fixture.