This campground is ideal: close to town, backcountry seclusion. The hike is steep, but manageable. Read about the hike here; 3.4mi, 1500ft + gain. Starts from the top of Bridal Veil Falls, so either drive up the switchbacks at the end of town or be prepared for the dusty hike up.
If I remember correctly there may actually be an old campsite grill up there. But don't count on it.
There are several patches of firm, clear earth for camping.
Catching sunset in the San Juans on the edge of an alpine lake at 12,500ft is as great as it sounds.