There are several options with this hike, including driving to within 150 metres of Governor's Chair Lookout, doing a 3.2 km return heritage trail hike or doing an 8.1 km circuit that also includes the lookout and heritage trail. This track is rough and there is one short steep section but really work doing.
The circuit starts at Spices Gap Camping Area off Spicers Gap Road and I recommend following the track in an anticlockwise manner. There is one section which requires scrambling and my feeling it is easier going up that section than down it. It also means that Governor's Chair, which has the best views, is closer to the end of the hike.
The initial section of the hike will take you through varied terrain and vegetation. You will also get great views of Mt Mitchell.
View of Mt Mitchell, another great hiking location
The heritage trail goes through more open country and you will be walking across an old stone road laid down over hundred years ago before Mt Mathieson become a national park. There is also the remains of an old bullock cart along the trail. Other places along the total circuit include an old well and a settlers grave yard.
Old bullock cart on the Mt Mathieson Heritage Trail