Spring and summer are mild, with temperatures ranging 60-77 F/16-25 C. It can be windy and wet at times, so carry an umbrella and jacket. Fall gets cool (40-60 F/5-15 C), and winter is dark and cold though dry, with temperatures from 40 F/5 C to well below freezing.
Stockholm's rainy season is June-November, when an average of 2-3 in/5-8 cm of precipitation falls each month. Some snow falls in the city from November through March. There's typically never more than a few inches/centimeters on the ground, however, and major streets are kept clear.
The best time to visit is May-August, though some smaller businesses close for vacation in July.