Welcome to Alaska----Anchorage basically has two ports the cruise lines use; Whittier is very close to Anchorage in the northwest corner of Prince William Sound and Seward is further south at the head of Resurrection Bay, which connects directly to the North Pacific (Gulf of Alaska). Actually, Anchorage does have its own port too but it is used mainly by freighters (Happens to be the largest port in the entire State though). Cruise Ships can and do use it but mainly as an intermediate port, rarely do they use it for embarkations and disembarkations.
Reason for that is Anchorage is located at the head of Cook Inlet which puts it pretty far north of the main Pacific Coast, meaning a lot of sailing time is entailed to get here which really cuts into the average week long cruise often marketed for Central Alaska originating or terminating in Vancouver or Seattle.
Cruise Lines generally use one port or another, but not both. I know Princess uses Whittier and HAL Seward.
Whittier is a relatively small recreational fishing port with some limited commercial fishing working out of there. It is a really small community. Whittier was originally started as an Army base and supply port during the war and two long railroad tunnels were necessary to connect it with Anchorage and the two large military bases here. Today, the tunnels have been modified so they accommodate both railroad and vehicle traffic, however, traffic is only one way, meaning it is controlled so it flows only one direction at a time, vehicles might have to wait a bit sometimes before they get a chance. Not counting the tunnel wait, it only takes a hour or so to drive down there from Anchorage. Seward takes at least two.
In other words, there isn't a lot to do in Whittier, however tour boats work out of there in the summer and that area has some pretty fascinating scenery. If you can work it out, get there early and take the "26 Glacier Cruise", which coincides with the cruise line schedules I understand.