Well... there is nothing to do in Whittier.. its a sleepy little fishign village. There are some excursions to local glaciers...
We rented a couple of cars there and drove to Anchorage for our fights. Ours were later than yours. We stopped at an animal refuge/zoo and then some of us went golfing and others toured anchorage (We had 3 car loads). Its about a 2 hour drive, so you have plenty of time to take in the sites. You will probably be docked in Whittier before you go to bed.
Carnival Cruise Lines:
Fantasy 90, Celebration 95, Victory 05, Conquest 05, Spirit 6/06, Freedom 6/08, Holiday 7/08, Victory 6/09, Valor 9/09, Dream 6/10, Splendor 8/10,Conquest 8/11,Magic 11/11,Triumph 4/12,Spirit 7/12,Freedom 11/12, Triumph 2/13 - The fire cruise
NCL Dream October 2006, RCCL Mariner OTS June 2007, Celebrity Silhouette 2013