With a family of six, we enjoyed renting the house on the hill in Lidingo, just outside of Stockholm. A hotel would have been way too expensive, and fortunately this house was fair priced and quite cozy! The house was a great choice because we could grocery shop and save money by eating meals at home. We were worried about commuting to the city from the house, but the trains in Stockholm are frequent and easy to catch. The house is one block from the train station (but you don't hear trains when you sleep--I promise!) and it's just two trains to get to central station.
I recommend getting the Stockholm card so you can have unlimited transportation on trains, boats and busses as well as all 80+ museums in Stockholm. It pays for itself after the first day!
Also be sure to visit Gamla Stan for a trip to the 17th century :)