Along the east rim drive New Hance to S. Kaibab or the Tanner to New Hance (Escalante Route) both might satify your interests. Tanner to New Hance the more difficult.
New Hance to S. Kaibab. Stay a night at the Beach. Then over to camp at Hance Creek, atop Horseshoe Mesa, or at Cottonwood Creek (or dry camp out along the Tonto on a river overlook). 3rd night, probably Cremation (give advice on water), and then up the S. Kaibab.
Escalante. Tanner Beach, Papago, Red Canyon (about 1.5 miles up from the Colorado where the spring is running (and before the trail starts the climb out). If you are big milers then can stop at Tanner Beach or Cardenas Creek, the beach at the base of the New Hance trail, then over to Hance Creek or Horseshoe Mesa and out the Grandview.
Out "west" give the Boucher to Hermit Loop a look. Camping-wise would stop at Boucher Creek, and then Monument. If you want to make a 4 day trip out of it layover and explore around Boucher.