After running the Middle Fork's Oregon Hole Gorge, a great way to top-off the day with more challenging whitewater is the South Fork of the Smith's lower gorge. This 1.5 mile run is fast, fun, and big. Rafting it is a test of technical ability and kayaking it is no less of a challenge.
To get to the put-in, cross the bridge going over the South Fork and make an immediate left. Travel on this road for about 1.5 miles and keep an eye out for a big pull-out on the left. Once found, there is a trail that eases down to the river. In rafts this can be tricky and another option is to put in upstream, run the main section (class III with one IV, 30 feet per mile) and then continue down into the gorge. With time-constraints, however, just muscle-up and hike your stuff to the river. The first part of the run is relatively quiet and without consequence. Upon reaching the first real horizon line, get out and take a look.
Your first time down in a raft you will probably want flows ranging between 500 and 2000 CFS. Make sure you have a small boat (probably 12' or smaller) unless you've got more water. Taking out with a raft just above the confluence with the Middle Fork is doable but not fun. There is a better alternative if you are willing to float a few miles on the Middle Fork.
Current flow for the South Fork Smith near Hiouchi (courtesy of Dream Flows):

More South Fork Smith information at Kevsmom.com