I would blast up to Bryce a few days there or the general area. Bryce has some good hiking, is higher in elevation (ie cooler) can be mostly seen in a single day or dang near every bit of it in two
We like Bryce Much more than the South Rim, indeed we much prefer the north Rim and can easily find weeks of stuff to do there. But we drive the back roads, take the trip to Toroweap and lots of other places. Not as much of that on the South Rim. That I know of that is,I'm not as familiar with the SR.
If you hike down to the river you better be in really good hiking condition and even more so Rim to Rim. And make sure to get reservation down at the river before you leave. The rangers are not amused down there if you do not. You can ride the mules down if you are under the weight limit.