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A 2 hour drive south of Anchorage is Seward, where there are several kayaking companies which will take you out into Resurrection Bay. People often see a variety of wildlife on these excursions, such as humpbacks, orcas, sea lions, jellyfish, etc. A cool kayaking trip from Seward is to Caines Head recreation area, where you can hike through boreal forest up to an old abandoned World War 2 fort with beautiful views of the bay. Homer is about 3 hours south of Anchorage and is also a good place for sea kayaking.

I personally have more experience with packrafting, which I highly recommend. High quality lightweight packrafts can easily be carried on/in a day pack. A recent packrafting trip I did: drive 1 hour south of Anchorage to Portage railroad stop, take the train 20 minutes south to the Spencer Glacier stop, paddle around the lagoon adjacent to the glacier (don't get too close, it calves frequently and can be quite dangerous), then paddle all the way back to the car on the Placer River (not a technical river)... about 8 hours total trip time.