Baltic Hostel is a smokers heaven. Finally a hostel where you are allowed to smoke indoors (except on breakfast time). Great place just next to the railway and bus station. 3-Maja Street #25, +48-58-7219657, online booking.
Hostel Targ Rybny is in directly in the city center. Grodzka Street 21, +48-58-3015627, gdanskhostel@hotmail.com, online booking.
Villa Sart in Gdańsk-Oliwa is a good an quiet place. I paid just 110 PLN per night for a very nice double-room in April 2008. uł. Wąsowicza 2A, +48-510510700, VillaSart@gmail.com
A good source of information about what to do in in the city is Gdansk In Your Pocket.
As not everybody is speaking English in Poland and as you don't want to feel stupid by not even knowing how to say 'Hello' in Polish, print yourself a copy of the Pocket Talk English - Polish micro dictionary.