There are 24-hour, 72-hour, and 7-day travel cards in Stockholm. The first two are valid for the indicated number of hours; the last is good for seven calendar days. The 24-hour card costs SEK 165 (about equal to 4-1/2 single tickets); the 72-hour card, SEK 330 (about 8-1/2 single tickets); the 7-day card, SEK 430 (about 11-1/2 single tickets).
Because of Stockholm's geography (spread across a lot of islands, with considerable distances sometimes involved), I used more public transit than I usually do. Among the places I'd consider beyond walking distance from most lodgings in the city are Millesgarden (well to the northeast on Lidingo) and Thielska Galleriet and Waldemarsudde in central and eastern Djurgarden. Liljevalchs and other (and better-known) destinations in western Djurgarden are easier to reach on foot, but still possibly beyond the distance most folks would choose to walk if not staying in the southern part of Ostermalm.
I stayed on Gamla Stan, which is very centrally located, but I went to quite a few obscure, distant places. I think I ended up buying a 7-day pass for my 12-night stay and pushing all my excusions requiring transit into the 7-day validity period of the pass. I was pleased at how much I got around a city with expensive transit tickets for such a moderate cost.
Some of the Metro stations in Stockholm have interesting art. I took several rides just for the purpose of seeing the stations.
Edited to add the critical worlds "in Stockholm" to the first sentence.
