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I'd recomend a place called Husman. It's in Kista, so it's neither in Östermalm nor Södermalm, but using the subway you'll get there pretty quick. The main reason why I'd recommend it is because they specialize in serving Swedish food, which can be hard to find for a reasonable price in Sweden as Swedes tend to go for exotic meals when going out. Here you'll get yourself a fine piece of herring or why not some Swedish meatballs with mashed potatoes? A lunch is 69 Swedish kronor, and in that price crisp bread, sallad and lingonberry juice is included...
Note that this is not a fancy restaurant, but rather a part of a large food court, but I'd say it's well worth visiting if you want to try something you probably wont eat at home...
