Allow me to warn you about how time-consuming two of the (wonderful) local museums can be if you are interested in their subject matter. The Solidarity Center took me well over half a day, and the new World War II Museum was 20 hours. I realize the latter was extreme, but it's an indication of how much English-language information (and English-subtitled video) is available at that museum. If you can allow only an hour or two to see one of those museums, I'd generally recommend the Solidarity Center, because I believe a short visit to the WW II Museum would be more difficult to strategize. I also ran into a bit of a wait at the ticket counter of the WW II Museum on one of my visits. Perhaps because it is relatively new, it's getting a lot of visitors.
If you're more into seeing pretty things, there's an amber museum in the historic center that I liked. Gdansk is so gorgeous that it's great just to walk up and down the streets.