wntrhwk, when you search, you should use the phrase "dispersed camping". I never tried more than overnight camping in the area, but some of the 14ers have 4wd access roads, where you might camp in the forest, namely Antero, Princeton, and Massive (all easy roads), plus there is a large 4wd area (easy) to the south of Rte 82 at the bottom of Independence Pass. You can also go back behind Homestake Reservoir n.w. of Leadville. Hike up to Holy Cross City (don't drive in that road). Nice area for hiking.
There is an area on the east side of the river down near Buena Vista very popular with boondockers. Elephant Rock, as I recall. Road 371.