Advanced Search results: Denali hiking, backcountry hiking
Useful day trip or backcountry trip info previously posted and useful for visitors:

Day trips-Denali vicinity:

Backcountry trips: many good ideas in Southcentral Alaska: Excellent info from 1sttimestar.

Hiking-backpacking: Denali Hwy : this one mainly on the Jack River area, includes the particulars of getting AHTNA permit

Tangle Lakes area trail map (see denalihunter, post#6):

Day hikes: Anchorage vicinity including good sources for more info:

3-4 day trips: Anchorage area: Good suggestion from Brian M for most visitors experienced in backcountry but new to Alaska.

(Much) more on Crow Pass:

Good luck!