The absolute cheapest way of sleeping is to become a member on couchsurfing.com and find locals that wants to give you a free bed in their homes. But don't do it only to save money.
I think hostels.com is the best site for hostel-booking. Most dorm beds in Stockholm costs over 200 kr per night. But, there are hostels in old boats, old prisons, summer-free schools and one in an old airplane, and that's pretty cool.
INTERNET ACCESS:
List of Stockholm addresses with free wireless connections.
The only internet cafe you need to know about - for surfing without plugging in stuff or print pages* - is Sidewalk Express. You buy a password for 20 kr per hour (in a machine or from the staff) and then you can log off and on as many times as you like at their computers around town. There are Sidewalk computers inside many 7-Eleven and Pressbyrån stores, at the long-distance train station (next to Burger King) and at the airports. This link shows that there are Sidewalk Express computers at around 60 different places in the inner city. Unfortunately you can't print pages from or plug in anything to the Sidewalk Express computers.
* "Regular internet cafes (= with a lot of game-playing teenage boys), where you should be able to plug in stuff and print pages: SouthPoint at Götgatan 101 and Matrix within the Hötorget subway station (exit name: Konserthuset). Another one (but one report told me that they don't print out): Zkillz at Saltmätargatan 9.
TELEPHONE CALLS:
There's barely no payphones in Sweden, and the ones that exists are not very cheap. So try using Skype's pay service SkypeOut if you can.
Special Telia payphone cards (value and price: 50 kr) can be bought in the Pressbyrån stores (in the long-distance train station, for example) and in the ICA supermarkets. Prices in the machines that accepts both coins and cards (there's also machines that takes cards only, and they can have different prices), as of may 2009: Calling a swedish landline phone with Telia card/coins/credit card: first 5 kr/10 kr/8 kr for five minutes and then 2 kr per minute. Calling a swedish mobile phone with Telia card/coins/credit card: first 5 kr/10 kr/8 kr for ONE minute and then 6 kr per minute. The only thing I can say about international calls is that you should add a couple of hundred %.
TOILETS:
Practically all toilets* cost 5 kr to get in to. For a list of public or semi-public toilets, go to toalett.nu and see the page for each inner-city district (from "Djurgården" to "Södermalm"). It's in swedish, but you can understand what the address is. (* The male urinals in the city toilet arrangements are free.)
BUYING ALL KINDS OF PRACTICAL STUFF:
Here are places for buying everything, the things you didn't thought of buying at home when planning the trip, or things to replace broken and lost items:
As much "everything" as it gets in general (but more household items than tools):
Åhlens at Klarabergsgatan. It's a giant department store. (Opening hours: Mon-fri 10-20, sat 10-19, sun 11-18.) Go to the subway station T-centralen and choose the exit that says Sergels torg. Åhlens has an entrance on the subway level. If you are walking, it's the big brown building at the crossing with Drottninggatan. If you don't find what you are looking for here, go to this place:
Smaller store than Åhlens, but very "everything" in the "man stuff" category:
Clas Ohlson in the mall Gallerian at Hamngatan. It's simply a big store for a lot of practical stuff: laptop bags, alarm clocks, tools, for example. (Opening hours: Mon-fri 10-19, sat 10-18, sun 11-17.) To get to Clas Ohlson, go to the subway station T-centralen and choose the exit that says Sergels torg. When standing on the round square you should go towards the glass obelisk, to get to Hamngatan, either on the upper level (above the square) or through the right-handed part of the walkpath. The mall has a smaller entrance in the walkpath and a bigger one (with the sign "GALLERIAN") above ground. The Clas Ohlson store is at the upper level of the mall. If you happen to be at the blue subway line, you can go straight to the subway station Kungsträdgården and choose the exit that says Gallerian.
Very cheap and pretty alround department store, but no guarantees, because they only sell "leftovers" (not second hand, but stuff that has gone out of stock at other stores):
Överskottsbolaget (ÖoB) at Fleminggatan 81. Go to the subway station Fridhemsplan and choose the exit that says S:t Eriksgatan. The store is in the crossing of the two big streets Fleminggatan and S:t Eriksgatan.
Extremely cheap and somewhat alround second hand-store, but no guarantees, because they only sell what people have dumped there:
Åter Vinnarna at Götgatan 105. Go to the subway station Skanstull and choose the exit that says Skanstull. You will get up near the point where the big streets of Götgatan and Ringvägen intersects. You should walk towards the bridge to the Globe and you should cross at least one road.
BUYING ALL KINDS OF PRACTICAL STUFF:
Here are places for buying everything, the things you didn't thought of buying at home when planning the trip, or things to replace broken and lost items:
As much "everything" as it gets in general (but more household items than tools):
Åhlens at Klarabergsgatan. It's a giant department store. (Opening hours: Mon-fri 10-20, sat 10-19, sun 11-18.) Go to the subway station T-centralen and choose the exit that says Sergels torg. Åhlens has an entrance on the subway level. If you are walking, it's the big brown building at the crossing with Drottninggatan. If you don't find what you are looking for here, go to this place:
Smaller store than Åhlens, but very "everything" in the "man stuff" category:
Clas Ohlson in the mall Gallerian at Hamngatan. It's simply a big store for a lot of practical stuff: laptop bags, alarm clocks, tools, for example. (Opening hours: Mon-fri 10-19, sat 10-18, sun 11-17.) To get to Clas Ohlson, go to the subway station T-centralen and choose the exit that says Sergels torg. When standing on the round square you should go towards the glass obelisk, to get to Hamngatan, either on the upper level (above the square) or through the right-handed part of the walkpath. The mall has a smaller entrance in the walkpath and a bigger one (with the sign "GALLERIAN") above ground. The Clas Ohlson store is at the upper level of the mall. If you happen to be at the blue subway line, you can go straight to the subway station Kungsträdgården and choose the exit that says Gallerian.
Very cheap and pretty alround department store, but no guarantees, because they only sell "leftovers" (not second hand, but stuff that has gone out of stock at other stores):
Överskottsbolaget (ÖoB) at Fleminggatan 81. Go to the subway station Fridhemsplan and choose the exit that says S:t Eriksgatan. The store is in the crossing of the two big streets Fleminggatan and S:t Eriksgatan.
Extremely cheap and somewhat alround second hand-store, but no guarantees, because they only sell what people have dumped there:
Åter Vinnarna at Götgatan 105. Go to the subway station Skanstull and choose the exit that says Skanstull. You will get up near the point where the big streets of Götgatan and Ringvägen intersects. You should walk towards the bridge to the Globe and you should cross at least one road.