to steer this away from sausages here are some more tips for visiting the city.
The city is really big in terms of area: the population is about 2 million but because of all the water and because Sweden is a huge, empty country, it spreads out for miles and miles. So careful to stay somewhere fairly central: most of the suburbs are pretty boring. The centre itself is small enough to walk in a day with time for lunch and coffee.
Here's a little map of the centre, the actual "city" area:
One thing you should know is that you should avoid the very centre of the city, around the central station and metro terminus T-Centralen. Not because it's particularly dodgy, but just because there's nothing to do or see there. Office buildings, high street stores, fast food chains and some of the city's ugliest architecture. As Geezee said, the big Kulturhuset is worth a visit if you are there, as they sometimes have some good exhibitions on.
The little built-up island right in the middle is Gamla Stan - quite literally "the Old Town" - which is the main tourist draw. There is one long street, Västerlånggatan, rammed with tourists and souvenir shops and cheap restaurants, so don't bother with that. The rest of the island is perfectly-preserved medieval alleys and houses with some more quaint, authentic craftsy and artsy shops and things. There are a couple of churches, and on the north end of the island are the royal palace and parliament buildings, while on the tiny Riddarholmen island (the little blob on the west side of Gamla Stan) there's a big cathedral where all the old kings are buried.
The next island to the east is Skeppsholmen, which you can reach by ferry from the bottom corner of Gamla Stan, or by bridge from the waterfront in the city. Here you will find the museum of modern art, architecture and design, which has a decent permanent collection and guest exhibitions of varying quality, and some other worthwhile museums (if you're there for a full week). The larger, greener one east of this is Djurgården, home of the huge open-air Skansen, which has a Nordic zoo and lots of transplanted homes and workshops from 19th-century Sweden, replete with folk in traditional clothing doing traditional baking, carpentry and what have you.
Elsewhere on Djurgården you can visit the Vasa Museum, with the world's oldest preserved sailing ship, which sank in the harbour on its maiden voyage in the 17th century. The built-up part of Djurgården also has your first port of call, the ABBA museum, plus the theme park Gröna Lund, the Spirit Museum, and Junibacken, a museum/playhouse devoted to Nordic children's literature (Pippi Långstrump, the Moomins etc). Much of the rest of Djurgården is pleasantly green and full of strolling locals, with the odd cafe or art museum dotted around.
The northeast part of the city centre is the swanky Östermalm district, full of fancy boutiques, classy restaurants and snobby people with slicked-back hair and suits drinking champagne. The architecture is very grand and it's worth a walk around though as Geezee noted the impressive food market is closed for renovation.
South of the centre is Södermalm which is grubby but gentrified. It's full of hipsters but has a lot of great places to eat and drink, some interesting shops and is really nice for walking around: not as pretty as Östermalm for the most part but with some lovely old cobbled streets up on the waterfront cliffs (ask for directions to Marieberget), which get a bit of tourist traffic due to the Stieg Larsson books. The SoFo area, the southeast part of the island (near the Sofia church up on the hill), is the trendy part for eating and drinking and shopping but there are also good places around Mariatorget and Hornstull. Near Slussen, the main transport terminus just over the bridge from Gamla Stan, is the popular Fotografiska museum*, which has a stylish building, a great restaurant and cafe, and an annoying tendency to focus on bland celebrity photography rather than more interesting exhibitions. Check what's on to see if it appeals.
The main northern part of the city is not so interesting, as noted before, but Vasastan at the top is pleasant: you have the impressive city library building, some parks and more personality in the shops and eateries. Across the bridge to the west is Kungsholmen, which is a pleasant residential area but nothing inspirational for a visitor; it's worth going there to look at the city hall (where they do the Nobel ceremonies) and stroll along the waterfront.
Heading northeast, the university has the Natural History Museum - decent museum but which could do with sprucing up - and the very pleasant Botanical Gardens, which are worth a visit if the weather's good (there's a great cafe there too).
The big palace at Drottningholm is a way out to the west. There are tours, I think.
Further afield Geezee already mentioned Artipelag and Millesgården as being worth a visit; the former is quite a way out to the southeast so check if the exhibitions really interest you, and if the weather's good: part of the appeal is walking around the cliffs and forest where it's situated. A friend of mine does the posters and videos for their exhibitions, just on a note of personal interest. Millesgården is easier to get to: you get the metro to the end of the line at Ropsten then hop on the local tram across the bridge.
Being a capital there are lots of other museums - several of them out in the "Museum town" east of Östermalm, past the embassies - and tourist attractions so it's perhaps worth browsing a bit and seeing what interests you. If you're there a week you have plenty of time to see the actual city - the centre isn't so big - and find other things to do.
You say you don't want to eat out too much but it's very much worth visiting a cafe or two. The Swedish way of life revolves around stopping for coffee, buns, cake, coffee and cake or buns, not having coffee or cake or buns but taking a break possibly in the vicinity of coffee and cake or buns, and they have some really good cafes. Some of the best are Mellqvist near St Eriksplan, Petrus near Mariatorget, Enskedeparkens Bageri at Enskede Gård (a bit south of the city).
If you just want general eating/coffee tips it could be worth downloading the app for the White Guide, a guide to the best eateries and cafes in the Nordic countries. I think you can get it in English (though it might only be available once you're actually in the region) but in any case you can call up a map with all the recommendations to see what's nearby, and it's usually reliable. It's a city full of great places to eat, however disparaging I may be about the sausages and potatoes.
*people will point out that it's not officially a museum as it's run for profit and has no permanent collection.