Looking back at Redfish from Thompson summit (courtesy summitpost.org)
Thompson is the highest peak in the Sawtooths, so it attracts a fair bit of attention, and Hyndman is the 9th highest peak in Idaho, and the highest point in the Pioneers. So you can count on fantastic views from either summit.
Details on climbing both mountains can be found in Tom Lopez's guide, Idaho: A Climber's Guide, available on amazon.com. There also are excellent detailed reports about climbing both mountains on Idahosummits.com and summitpost.com.
An adventuresome friend of mine, Steve Townsley, took his two boys to the top of Hyndman Peak when they were 10 and 12. Steve says the rapid elevation gain involved in climbing to Hyndman was hard on the boys, giving them headaches and making them nauseous. If you're planning on taking kids, even most 12-year-olds would have a hard time climbing Hyndman. The kids -- and you -- need to be in good shape, and highly motivated to make it to the top.
It's a good idea to camp at the base of Cobb and Hyndman Peaks the day before, and acclimate to the elevation before heading to the summit. Hyndman is located in the East Fork of the Big Wood River drainage. You head up the East Fork, past Triumph, then go left on the jeep trail heading up Hyndman Creek to the trailhead. Follow directions on the Idaho Summits web site on approaching Hyndman Peak. There is a yurt platform in the trees at the base of the mountain peaks where it's ideal to camp.
Thompson Peak is best accessed from the Redfish Lake Trailhead near Redfish Lake, Stanley and Idaho Highway 75. It's 6.5 miles to the summit and 4,200 feet of elevation gain. Again, it's best to hike into the base area of the peak the day before heading for the summit to acclimate to the elevation and to give yourself some time to enjoy the spectacular scenery.
The key when heading to the summit of Thompson is to corkscrew in a counter-clockwise direction toward the west and south portions of the rocky peak so you don't get cliffed out. This is the best way to approach the summit for the easiest but still difficult walk-up route.
Enjoy! - SS