The Hayden Spires are a cluster of alpine towers approximately 3 miles NW of Notchtop. There is Hayden Spire itself, which is the high point of the massif, East Pinnacle, and Hayden Lake Pinnacle. There are other smaller unnamed summits, too.
These are arguably among the most remote summits in the Park, offering decent rock with a degree of solitude. One can view this area easily from Trail Ridge Road, at the Forest Canyon overlook. The Hayden Spires are flanked by two alpine lakes, Lonesome Lake on the east side, and Hayden Lake on the west. The rock is of the standard alpine quality found in most of the Park.
There are 3 approach options for getting to the Hayden Spires. All of them are long enough you will likely want to bivy.
1st option: approaches from Bear Lake. Hike to the top of Flattop Mountain, and then head north on the Tonahutu Creek trail for about 2 miles. Then when the trail begins to descend to the northwest, head north on Bighorn Flats to Sprague Pass and then Sprague Mountain. If you seek routes on the southeast or east side of the massif, traverse to the east side of Sprague mtn. where there is a small pass, and descend to Lonesome Lake. About 8 miles, 4,000 vertical.
2nd option: Begin at the Fern Lake trailhead, and hike to Spruce Lake. Head NW from Spruce Lake and then west up Spruce Canyon to Sprague Pass. This route is a bit shorter, but has more vertical gain. Also, you have no trail once you leave Spruce Lake, but the solitude and terrain are very nice. 6.5 miles to Sprague Pass.
3rd option: approach from Milner Pass along the Divide. At least 8 miles.