I totally cheated and used a map, and still only got 7! Most of the ones on the map didn't make this list. Looks like they are mostly in the Greater Salt Lake City area.
I tried Taylorville, Taylorton, Taylortown, Taylor City...I knew those were close, but just forget the "s". I guess there is more than one Taylor living in the town. :)
Knew SLC and got one by chance