Stockholm is not an easy place to eat on a budget. Food can be expensive, and supermarkets are few and far between in the central town. There is the usual mixture of multi-global burger bars, pizza houses, and chicken takeouts, which will keep you going, but for something more substantial, you have to dig fairly deep.
Local food is generally wholesome, hearty, and basic--meats, stews, and soups being particularly favoured.
The best bet is to look out for the lunchtime specials which most of the restaurants now have, which will include bread, main meal, pudding, and coffee for a considerable discount on the evening price. I have to say, the food I did eat in Stockholm was not that great, often arriving at the table lukewarm. Some of the big department stores offer the best deals, if you actually manage to find the restaurant in the store.
Drinking is almost a sport in Stockholm, but prohibitively expensive too. Most pubs and bars will charge you to "look after your coat," or in other words, charge you to get in. However, there are enough pubs along the main Drottingsagten to whet anyone's appetite.