I have an old bike that my wife would like to get back riding now that we are near a bike trail. The tires on the bike are dry rot and I need to replace. Tire size is 26 x 1.6 having troubles finding a match. Any alternatives?
The late great Sheldon Brown's web site has a page on tire sizing that says your wife's tires have a 559 mm "bead seat diameter" (BSD). The BSD way of measuring tires is unequivocal and cuts through a lot of the confusion with tire sizes, although the clerk at your local bicycle shop probably understands 26 x 1.6 better.
Anyway, Sheldon's page goes on to say that tires sized anywhere from a 26 x 1.00 to a 26 x 5.0, where the number after the x has a decimal point and not a fraction, should fit the rim. Of course the tire also has to be able to squeeze between the brake shoes and not rub on the frame, so some of the wider tires in that range, such as a 26 x 5.0, probably would't work.
If you take the bike to your local bike shop, meaning a locally-owned shop, not the bike department of a department store and not a store that's part of a big chain, then they should be able to help you. Bring the whole bike so that they can test that the tire fits between the brake shoes and doesn't rub on the frame. Good luck, and happy riding!