it'll be around 100 miles if you don't get the second shuttle and hike/bike from the east entrance to chamberlain ranch.
otherwise, i would recommend combining a few shorter hikes. buckskin gulch/paria is good. keep an eye out for a permit opening up, or just do it in a day.
Bryce canyon's under the rim trail is in prime season right now too.
Owl and fish canyon is pretty awesome.
Salt creek in canyonlands is also very fun. The needles is a blast.
Coyote Gulch and the escalante river is a great shuttle hike.
Capitol reef is pretty off the map, and has some great backpacking.