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Why pick up the car on Sunday Aug 14 if you are mostly going be in Anchorage that day? You might save enough money on the rental if you pick up on Monday to pay for the cost of a shuttle to Flattop and back. It is worth comparing anyway.

Aug 16 is too much. You won't get to Harding Icefield Trail until well after 6pm. It takes 6-8 hours to hike the entire trail. I would do Sealife Center this evening (open till 8pm?). Stop at Exit Glacier the morning of Aug 17th on the way to Whittier. But you really don't have time for hiking Harding Icefield Trail.

>>August 18: Drive to Denali State Park. Kayaking Byers lake. Drive to Denali National Park entrance. Hike Denali Horseshoe lake trail.

Kind of a long day but it would work. Be sure to buy grocery food for Denali in Anchorage or Wasilla.

>>August 19: Take shuttle bus to Wonder lake. Hike Eielson Alpine trail.

I personally would strongly advise doing a different hike. Why, with all the vastness of Denali NP, do people like hiking with dozens of others on this trail? Hike down to the river bar from Eielson. Or hike the mountain to the east of this alpine trail. Or ask a bus driver for other ideas. I guess if you like crowds and like being a "tourist" do as planned. But certainly not my suggestion.

>>August 20: Take shuttle bus to Wonder lake. Hike wonder lake trail and Eielson Stroll.

There is no "Wonder Lake trail." Do you mean the McKinley Bar Trail? If so, be sure to let your driver know you are doing that and he can let you off at the trailhead. That saves 1/2 mile of walking.

Be sure to bring a bus schedule with you

>>August 21: half day in Denali NP. See whether I can book discovery hike. drive back to Anchorage.

Disco Hike won't work unless you have more time. Try to get to Denali by 8pm on Aug 18th and go IMMEDIATELY to the visitor center to check on Disco hike availability. They should be taking reservations for Aug 19 and 20 by then. Book whatever day you can get and whichever hike most interests you (hikes are posted by Friday online at nps.gov/dena). If 19/20 are full when you arrive on 18th, then when you return on 19th check again for the 21st. You can still do a Disco hike this day, just arriving in Anchorage later than planned.

If you really want to do the Harding Icefield Trail hike, why not depart on Aug 14 for Seward? Do the Harding Icefield Hike on Aug 15 before kayaking. Then Aug 22 you can do the Flattop hike, Tony Knowles and/or shopping.

Buy your shuttle tickets now to Wonder Lake for all three days in Denali. Call and get 3 bus tickets for the price of 2 (this offer is not available online). If you get the Disco hike one day, you can exchange your ticket for $4 at the WAC.