Since I spent 8 hours in Gdansk I had a game plan going in with time factored in for wandering & exploring. I know there's more to see but I wanted to see specific things and that worked fine. I was there in mid-May and it was a cold, gloomy day with rain arriving late in the afternoon.
My train arrived at 9:30 and using my map I easily found my way to the old town, out of the station and head right, 10 minute walk. I got to see a cheerleading competition, complete with bad pop music, explored a small street market and found a place for a roll and coffee before giving the old town a cursory exploration. The architecture is fascinating and I walked for a good hour, taking many photos. Around 11 I went out on a boat--like a pirate ship, very touristy but the best way to get out to the Westerplatte--I really needed to see where WWII began and you see the working shipyards as well. By 1 I was back on land and had lunch along the waterfront, plenty of interesting restaurants there. More wandering old town and then I headed back towards the train station, checked out the amber museum and a market hall on the way, and basically a 10 minute walk from the train station but heading left is the Solidarity gate and new museum. The museum is quite well-done and an interesting look at the solidarity movement not only in Poland but other countries under Communist rule. I spent a good 2+ hours there, had a snack and basically killed some time as it had begun to rain and I was dreading the walk back to the train station.
Overall I felt it was a perfect day--beautiful and unusual town (I've been to numerous medieval cities and many felt similar but Gdansk is different), and a chance to see the Westerplatte and the Solidarity sites.