Gdansk (and the rest of Tri-City) can easily afford several days of exploration, but for the visitors interested in day-trips out of the city, there are also plenty of opportunities. Pretty much all of the trips are doable by public transport, some more, some less easily.
The landscape of the regions surrounding Gdansk is surprisingly varied: depending on the way you go, you can find yourself in a gently rolling countryside of the lakeland, on the dunes of a sandy Baltic beach or on pancake-flat fields of a below-the-sea-level depression. One of the obvious destinations for a day or a weekend trip is the Hel peninsula.
(1) The Hel peninsula: a long sandbar closing the Bay of Gdansk from the north-east, it is a strangely appealing place dotted with several settlements– originally mostly fishing villages, but now almost exclusively devoted to serving the holiday industry which concentrates on sea and sand pursuits: from nudist beaches to windsurfing to fish-eating to visiting seal Sanctuary, there is something for everyone (if you can face the crowds). Easiest to reach from Gdynia by train, bus or boat. Small fishing towns north of Gdynia (like Puck) are also pleasant and easier to get to.
(2) The Vistula Lagoon and sandbar: opposite way and nearer to Gdansk than Hel, it is in some ways similar. Shabby resorts, fishing villages, decent beaches and bird watching possibilities (a great reserve in Gorki Wschodnie) and a promise of amber in the winter and spring storms (Mikoszewo). If you don't feel like going far, take a town bus to Gorki Zachodnie or Sobieszewo.
(3) Frombork. In the same rough direction as Vistula Sandbar – i.e. going east from Gdansk – this sleepy town attracts visitors by its grand Gothic cathedral complex and even more so by a connection with Nicholas Copernicus, who was a canon here and here conducted his observations that proved that the Sun and not the earth were the centre of the Solar System.
(4) Malbork. South of Gdansk, on the river Nogat, lies a small and shabby town of Malbork, famed for the vast complex of the brick Castle of the Teutonic Knights: if you are to see one castle in Poland, make it this one. Parts of the castle are only accessible to a tour, but the whole place is still arrestingly impressive and well worth visiting.
(5) Castle-baggers (especially those with a car) might consider adding several other Teutonic Knights' castles to their collection: Gniew, Kwidzyn and Golub Dobrzyn all have interesting if smaller (but much less busy) examples.
(6) South-east of Gdansk lies the region of Zulawy – a fertile agricultural flat, located partially in the floodplain of the Vistula, and partially formed of reclaimed land (the first to do serious work here were Dutch Mennonite settlers, feeling from religious persecution). It's not a conventionally beautiful or dramatic place, but it has a certain melancholy beauty and, being very much a tourist backwater, can offer a glimpse into somewhat forgotten history and somehow unrecognised present. Elblag is the main town, with a few sights or moderate attractiveness, but the interest is more in slow travelling through Zulawy.
(7) The wooded hills bordering the Tri-city to the south-west turn into the lakeland of Kaszubia. This is a region of gentle, rolling countryside, dotted with picturesque lakes and largely covered with forest. Many residents of the Tri-city have summer houses or plots of land here and it's a prime area for the locals to escape to in the summer, more so than the sea coast which is considered to be too crowded with tourists form the inland Poland. Kaszubia combines pleasant environment with unique folk traditions (the local dialect is more different from the standard Polish than some languages considered foreign) and developing infrastructure for active holidays, including horse-riding, kayaking, sailing and even skiing in the winter (although the highest hill – complete with a ski lift – is only 300m high). For a taste of old Kaszubia life, visit a skansen in Wdzydze Kiszewskie.