The Matterhorn (14,690') is certainly one of the most iconic summits on Earth. It is also a difficult climb, with no easy route to the summit. Ian Corless puts it this way:

Capitol Peak (14,130') is one of the harder of Colorado's 14ers.  The standard route, from the Capitol Creek TH, is 17 miles RT with 5300' of elevation gain, and some 4th class sections on the infamous "Knife Edge".  But, unlike most of the Elk Range the rock is quite good.
 

Old Speck is in Grafton Notch State Park.  It's about 7.6 miles round trip from the Old Speck Trail parking area to the top & back. The ascent has a Strava segment.

Challenger (8236') is at the northern end of the Pickets, a remote subrange of the north Cascades. The climb requires a fair bit of glacier travel and a few moves of 5.5 rock near the summit.

http://www.summitpost.org/mount-challenger/151237