There are some nice roads around Mormon Lake.
One of them comes up to the lake from the southeast. There is a rough fun section for several miles. I think it is FR 82 You can get to it off of AZ 87 about 25 miles south of Winslow.
Last year we took some really pleasant forest roads west of Mormon Lake and met up with Lake Mary road just outside of Flag.
The Mogollon Rim road south of Show Low is a good one that goes for about 100 miles if you did the whole thing.