Of the four wilderness areas close enough to my home for day hiking, the one to which we most frequently return is the Holy Cross Wilderness Area. Named for the Mount of the Holy Cross, and dominated by the Sawatch Range, the Holy Cross Wilderness Area is most easily accessed from the south via the Fryingpan River valley, and from the north via several roads leading out of the Eagle-Edwards-Avon corridor along I-70.
Some of our favorite hikes, including those we do annually, include:
Lyle and Mormon lakes
Savage Lakes (and the Savage-Carter loop)
Josephine Lake
Eagle Lake
Coming out of the Roaring Fork valley, these are the ones most accessible to us, but the area is rich with great trails, and contains some of the best scenery you'll find anywhere.