I present to you (from the perspective of someone who's only visited Stockholm once, remember, and with the caveat that it's surely very incomplete still--I haven't ever been to Pet Sounds, and I hear that's big)...
The Poster Girl guide to CD shopping in Stockholm
Keep in mind that these are not intended as real reviews of the overall quality of any of these stores--I'm writing about how much they fit what I was looking for and would be likely to appeal to people with taste similar to mine (I should note that I have no problem with buying used CDs and that I have no interest in vinyl). It's also worth keeping in mind that I was mainly visiting these places the week after Melodifestivalen weekend, a weekend during which many pop and schlager fans were buying everything they could and so may have drained many stores of their best pop CDs.
The big mainstream stores/stores run by big companies
Megastore (Sergels Torg; i.e., on the T-bana level in the big plaza that Kulturhuset also sits on)
The physical store version of the Internet store I use! A decent selection of new (in both the sense of unused and recently released) Swedish pop, with the Swedish music separated out from the rest of the music. Megastore had probably the biggest selection of singles I saw anywhere, too. There's a big section of discounted CDs, but the Swedish CDs aren't separated out and it can be a little frustrating to paw through--there are only so many times you can stare at budget compilations of music from the '70's or something before you just want to give the whole thing up. If you're patient, though, you may be rewarded: there's not a particularly big Swedish selection in among the big discount racks, but I did find Drömhus's Drömmar CD going for a very good price (well, I'm sure you could easily find it going for an incredibly cheap price on Tradera, but that's besides the point). I'd say it's good if you're looking for fairly recent pop CDs from the past couple of years or so.
Åhléns (Klarabergsgatan 50; you can also enter it via the aforementioned lower T-bana level of Sergels Torg if you cut through a little makeup selling area)
If you're looking for a brand new, just released today album, Åhléns is your best bet, though if it's a big release the other big mainstream stores will be likely to have it too. As you'd expect from a big mainstream store, there's a big selection of new pop CDs. You'll also sometimes find sales (some CDs marked down to 70-80 kr, for example), if the timing is right, and you can always count on their special sale bin, which has a 35 kr for one CD or 5 CDs for 100 kr deal. This particular Åhléns didn't have a particularly impressive selection in said bin (though you'd still find some good albums--Zandra's, for example), but others I've been in have had some great bargains if you don't own the albums already (Marie Serneholt's album, for example, which did make me sad, to be honest). If you're in Åhléns City near the T-Centralan T-bana station, the music is on the tunnelbana level (if you entered from the street level, it's the floor below you).
NK (I'm not sure what the official address for this is, but if you're wandering around the center of Stockholm you'll see it; you can also enter via that lower T-bana level of Sergels Torg, though you'll have to go back through this walkway area)
Up on the fourth floor of this department store is where you'll find their music selection. It's what you'd expect from a big mainstream store and it does have a discounted CD section, but you won't find too many bargains and looking for them isn't too time efficient given the payoff. Still, if you've got the time, definitely stop by and looking through their selection.
Bengans (Drottninggatan 20)
If you have more credible taste than I (or some specialized music taste--say, Japanese punk) and are still looking for a big mainstream store to go to, I think you'd love this place. Even if you don't, though, they've got some good pop CDs, though I didn't see any particular bargains and their selection of pop music isn't quite as big as you'll find in the other big mainstream stores.
The "used and new"/not run by a big company stores
Atlas CD Skivbörs (St Eriksgatan 78)
If you only have time for one of these not-run-by-a-big-company stores, I'd go with this one. In the big CD section, Swedish CDs are separated out from the rest of the CDs, making for easy browsing for the non-Swede who's not really concerned about CDs they can get elsewhere. As with the rest of the stores of this type, you'll find new CDs--in the sense of not used, not in the sense of recently released (though there are some of those, just not usually the released today ones and not going for any particular bargain)--are marked down significantly compared to what you'll find in the big mainstream stores, which usually have some discount section but usually keep even older new CDs at a higher price than they probably should be (take Lisa Miskovsky's self-titled debut album, for example; in the new mainstream stores I saw it in, it was going for more that 100 kr, something around 120-130 kr; in the smaller stores, it was going for 60 kr new). There may not be much schlager here, but fans of pop both on the cool side (Lamont, Cat5) and less cool side (Pandora, DeDe) will find a lot to buy. Expect most of the used albums to go for around 50 kr, but possibly the best thing about the store is the big 20 kr per CD section. Yes, it's not got the Swedish CDs separated out, but you'll quite easily find yourself leaving with a big stack of CDs courtesy of it.
Record Hunter (St Eriksgatan 70)
There's a new CD section on the first floor, but though you may want to give that a quick browse, the bargains come downstairs, from the section for used Swedish CDs. That used Swedish CD section may not look that big (the used international CD section definitely is), but you'll find loads of gems in it--despite Melodifestivalen just having happened and the schlager fans having generally bought out anything remotely Melodifestivalen or schlager-related, I still spotted albums from Charlotte Perrelli (I din röst, though), One More Time (Den vilda), Lena Philipsson (Fantasy, though, which seems to be stocked in just about every store in town), Sara Löfgren, and Sanna Nielsen (Nära mej, Nara dej). I wouldn't really say it's a schlager-heavy selection, though, but you'll find some good pop if you're looking for it. Expect used CDs to be about 40-60 kr, with many though not all being part of the "buy 3, get 1 free" deal.
Marquee Records (Odengatan 78)
Swedish CDs are not separated from the international CDs here, but the used CD section is worth a browse since you'll see some of the best used CD prices around (many--though not all--used CDs are 30 kr or less) and I saw some albums here that I didn't see anywhere else (they even had the Poets' single for "What Difference Does It Make," which I very nearly bought just so I could scan the over and show everyone what Jimmy Jansson looked like on the front of it--was that even him?). One international Swedish pop fan could pretty easily wipe out their selection of good used Swedish pop CDs, though, so beware if you're going in a group! Like the rest of these stores, their new (unused) but older CDs go cheaper than they would in one of the big mainstream stores, though not ridiculously cheap.
Wasa Skivbörs (Hälsingegatan 2)
Given the looks of this store, I was surprised at how easily I found schlager here: Lena Ph's "Lena 20 år" (admittedly not a rarity at all) was prominently displayed and they had a bunch of albums from Carola as well as Nanne's Alltid på väg). It's a small store, but the Swedish CDs are separated out from the rest of the CDs, making it easy to do a quick visit if you're in the area.
Went into but wouldn't really recommend/tell you to put near the top of your list
The Beat Goes On (St Eriksgatan 67) (this is the one out of the stores I went into that I think I can pretty much rule out going back to--if you're looking for Swedish music, you won't find very much of it at all here, and the emphasis is more on classic rock, I'd say)
RuntRunt (Odengatan 90) (if jazz is your thing--and it's not mine--I imagine this place might be a must visit; there's not really any pop at all [oh wait, I did see one copy of Carola's Främling, but I think that's literally it], though I can't say I didn't see artists I like--Laakso, for example; more on the rock/indie/jazz side of things).
