Denise - Whittier has been another port for Anchorage for years. But both Whittier and Seward require transport to or from Anchorage. Whittier is around 75 miles from Anchorage whereas Seward is around 127 miles.
The airport you must use is Ankorage. The trip from Ankorage to Seward is beautiful and if you have the right person giving naration it can be quite interesting. Also if you are lucky you may see a beluga whale, some moose or bears on the way.
There is an airport in Seward but there are no scheduled flights there from Anchorage. You would be flying into Ted Stevens Anchorage International Airport (ANC) then either staying in Anchorage or Transferring via bus or train. Neither Seward nor Whittier are ports for Anchorage. Anchorage has it's own port. It is just that more cargo goes to the Port of Anchorage. There is again a cruiseline porting in Anchorage, Cruisewest. They are a smaller line of ships. The one out of Anchorage will be cruising to eastern Russia to Nome and back with stopping where things are interesting to see (not necessarily at a port) as well as schedule port calls. Princess used to come straight to Anchorage.
I did some research and it seems to me that you would have to take an "air taxi" or charter a plane from Anchorage to Seward if you want to fly there...most take the train, drive, or cruiseline transfer.
There is a small air taxi service based in Anchorage called FS Air. Go to <http://www.fsairserviceinc.com> and you'll have all the information that you need. I've flown with them several times over the last 15 years or so and have been very happy with their service.
Shipmaven, it is probably the dockage fees that have them at Seward now. Whitter was dropped too until within the last couple months that the city council reversed their fee increase that drove the cruise lines away in the first place.