SL running public transport in Stockholm now has new tickets aimed to make it easier for tourists using public transport. The new paper based tickets are valid for 24 or 72 hours traveling in Stockholm. Staying in Stockholm city you probably only need the card valid for zone A. Please do not ask us how the different available cards work, SL are know for not making it easy to understand their ticket systems..
Basic price for 24 hours is 115 SEK and 230 SEK for 72 hours.