If you have the time, definitely hit up the payettes. The NF is one of the best runs in the west. Incredible ratio of action to downtime (shuttling/flatwater). Just as others have said, start on the lower, then move to the upper and then the whole enchilada. The upper and lower both give you some time between rapids. There isn't anything much harder in the middle compared to the upper EXCEPT that there is very little to no downtime between rapids in the middle. Traditionally the flow is calculated by taking the Main Payette at Horseshoe and subtracting: SF at lowman, deadwood below deadwood res, and MF at crouch. Right now, the NF below cascade gauge reads real close to this, but I seem to recall that it has differed substantially in the past. You can get the est flow w/out the math from Phateye.com and going to their Idaho flow page.
Some other possibilities as you make the trip west... As mentioned earlier, the deadwood may be running. It is a loooooong shuttle and well worth paying someone to drive your car back to the take out if you decide to do it. Try asking about a shuttle on the kayakidaho.com forum. I think you hook it up through one of the raft companies there. The run is 20+ miles but it moves relatively fast. It's scenic with about 4 or 5 class IV-IV+ drops. Unfortunately, some of the good rapids will likely have wood and need to be walked. Overall, I'd say it's worth it for the scenery, but not so much for the whitewater. Don't worry, you'll get plenty on the NF.
Other runs that are more or less "on the way" are:
-The murtaugh section of the snake. You'll literally drive right by it on your way to boise (fun, class IV play run). Nice pics and description here: http://www.oregonkayaking.net/rivers.../murtaugh.html
Word is that they will shut the water off sometime this month, but worth checking flows on your way out. You are looking for a min of 1200, take your playboat, there is a great hole about 1/3 the way into the run.
-Blackfoot river near blackfoot, id (just north of pocatello). This is a way underrated run. Good class IV+ with one class V-. Well worth the mandatory portage through poison ivy (bring some soap). If they are irrigating for the winter wheat crop in late august, you will likely have flow. Check the USGS gauge for blackfoot at shelley. That would be the minimum amount in the river. There may be as much as 175 cfs diverted above the gauge. You're looking for a min of 550 or so. PM me if you need more info.