There is an interesting Museum of Fishery in the 15th century Gothic St. Peter and Paul Church. From the top of the church tower you have a wonderful view other the city, the beaches and the sea. The museum is open 10AM-6PM.
At the south boulevard there is the Sealarium of the Gdansk University. There are performances for tourists but the goal of the basin is to grow the seals and to set them free. The seals are fed from 9AM-3PM.
Museum of Coastal Defense
with very interesting Blockhouses and exhibits. (http://www.helmuzeum.pl)An open-air-museum of the Polish Navy can also be visited from 9AM-4PM. You are allowed to enter the exhibits.
In the pine forest north-west of the city there are old WWII trenches and bunkers. You can climb right into the bunkers, but look out for the barbed wire strung along the ground in some places.