In 1998 we stayed at the Queen's Hotel on Drottninggatan 71A. This is the main pedestrian shopping street and if you walk down the street, you are at Gamla Stan (maybe a 15 minute walk). The produce market is near by. Doubles started at 550 kr with a bath down the hall in 1998.
On Gamla Stan, try eating at Kristina Restaurang (Vasterlanggatan 68) They have a three course and four course 'tourist' menu. We buy one of each and split the desert. It was reasonable and definitely Swedish.
There is a bus service (flybussen?) between the airport and City Terminal although I don't know the price. The TI at Sveirge House has the answer to everything. You might want a one-day Stockholm card which covers buses, underground and attractions. Get a guidebook from your library and try to get an idea of what appeals to you and is feasible. At some time, get out on the water and I highly recommend the VASA museum. City Hall tour is also interesting (Italy has its cathedrals but Scandinavia has its city halls).
Stockholm is definitely worth whatever time you can spend there.
Barbara in Connecticut