I use Dunlop Elite 4 Radial tires and recommend them.
(I’ve read that bias tires are available… I don’t know why someone would want them).

There are other options that I have no experience with. Most people (I think), and all the people that I know who ride GL1800 Goldwing use the same tire. I have no experience with “dark-side” tire options.

Part numbers are… Front: 130/70R18 and Rear: 180/60R16

Note that when mounting ensure that the direction of rotation is observed.

Tire change is the perfect time to replace valve stems. I recommend the non-OEM style fully metal 90 degree bend replacement. Chrome, nickel plate are available.

http://wingstuff.com/shop/?keyword=gl1800+valve+stems

Tires:

Amazon: https://www.amazon.com/EBC-Pads-Brake-FA261HH-FA261/dp/B0174K43JW

Wingstuff: http://wingstuff.com/products/37489-dunlop-elite-4-tire-combo-for-gl1800?from_search=1