There are also a couple of boat accommodations in Stockholm which might be a somewhat different experience and nice way to indulge in the 'water city'.
I have stayed at Gustaf af Klint, which was all good, great breakfast. They have both hostel and hotel accommodation options. It's located on the quays of the island Södermalm, which is only a 5 min. walk from the old town. The boats for Djurgården, with the tivoli (Gröna Lund), the zoo (Skansen) and many museums departs from Slussen which is practically next door.
There's also The Red Boat, haven't stayed there myself though.
Something I like to do when in Stockholm is having ice cream at Fjällgatan (which is on Södermalm, just above where the Gustaf af Klint hostel is). Follow the street until you find the little café and enjoy the splendid views of the city.
During the summer Stadsteatern (the city theatre) arranges Parkteatern (the park theatre) which is various free plays and performances in different parks around town. Most plays are in Swedish though, so is the schedule on the site, but might be nice spending a sunny evening in the park with some locals.
I also like visiting the Rosendal's gardens (www.rosendalstradgard.se) on Djurgården. They are the gardens of a former royal palace (musem today) and are open to the public. After a scenic stroll from the city center out to the gardens you can enjoy some delicious food in the café.
Happy travels!