Another nice hike in that general area is Escudilla. It is south of Eager/Springerville on US 191 There is a trail description here, along with some nice photos. this hike offers nice viewpoints of the area, a gorgeous aspen area -if the leaves are still on the trees- and some nice wildlife habitat. Baldy is also a beautiful hike, especially the lower sections, which run through meadows along the Little Colorado River. Unless you sneak up to the top (currently closed to non-Indians to the best of my knowlege) you will not get above treeline to enjoy the views, nor be able to do your victory dance on the actual summit.
Both trails can feature a bear encounter. Keep an eye on your dogs, and a leash handy just in case...-Randy.