I would say you are looking at at least a 60 mile trip. I am not sure of the rate for a taxi in Alaska, but I would say you are looking at at least $100. Might be less expensive to rent a car one way - or at least a dog sled.
Last night I read that there are buses that transport people from Whittier to Anchorage. we are only wondering, because we plan to stay a few extra days in Anchorage prior to or after the cruise. Planning to go next August or late July.
There are no taxis from Whittier to Anchorage. The cruiselines have buses and maybe a train. They do not have car rental there unless the major companies deliver them there for reserved rentals. Of course, you CAN book a limo to meet you in Whittier.