The Blackfoot wave in Firth makes for some good play all summer long.
A local gem that is not well know (at least 10 years ago) is the Fall River up near Aston, Idaho. It's got a great class III/III+ run about six miles long that starts in early May (depending on weather and snowpack) and runs late into the summer, turning into an awesome rock garden within a canyon, as long as you don't mind and can float the shallow first mile of the run before the canyon starts.
It's about an hour drive from Blackfoot. Put in is just past the Ashton Golf Course, stay on the main road (instead of turning to go to the Golf Course) and you'll cross a low bridge. That's the put in, the take out is the high bridge you crossed on the way up the river. There is a dam about 1/2 the way into the run, following a lake like section. Previously the dam has been runnable on one half - best to scout first.
The biggest rapid is down river from the dam and about 1 mile above the takeout at the high bridge. You can drive up a dirt road from the bridge to the small power plant (uses the dam further upstream) and from there you can walk upstream and scout the rapid.
You can also run the lower section, a class II like run with one decent rapid where the river crosses under the Main highway (the highway from Rexburg to Ashton) further down stream. A nice little rapid at the highway bridge, and a good surfing wave under that bridge at the right water levels.
A few miles from the highway bridge the river runs into the Chester Dam.