Summer — June through August — is far and away the best time to visit Pori. The days are long (the midnight sun doesn't quite reach this latitude, but it barely gets dark in June and July), Yyteri Beach is at its best, and the city comes alive. The Pori Jazz Festival in July is the main event, and if that falls within your trip, all the better.
Winter is cold, dark, and not especially remarkable for visitors. March and April bring more light and the chance of snow that is still usable for outdoor activities. Autumn — September and October — has its own melancholy Baltic charm, and the colours in Kirjurinluoto Park are excellent.