If you ever hesitate about going to Stockholm in autumn: don't, just book a trip, it is definitely worth it! Yes it's true that the short and bright nights are over in September and most of the outdoor-restaurants are closed. You might also have to wear some warm clothes and there might be some grey days. But that's basically it, for everything else autumn is maybe even my favorite season in Stockholm. When you're lucky to be there on a beautiful autumnday with sun and blue sky while the trees start to change colors, the city is ridiculously beautiful! Most attractions are open, check the slightly different opening hours before going. Djurgårdsfärjan still brings you to Skeppsholmen or Djurgården every 15 minutes until the end of September (less frequent afterwards) where you can for example walk along Djurgårdsbrunnskanalen or along the water through Nobelparken or enjoy the views from Skeppsholmen on Gamla stan or Strandvägen.
Absolutely visit Skansen, it's a bit like a fairytale in autumn with all the colorful houses and the colorful trees. They even have a yearly autumn-fair worth visiting.
For food, my favorite place in autumn is Rosendal's trädgård where you can still sit outside in the sun (even under colorful grapes) and then walk back to the tramway through the forest.
And if it should ever be grey and cold, there are many museums to visit in Stockholm. More information about some of them can be found on this page.
So you can definitely not go wrong with visiting Stockholm in autumn. You might even want to come back the following year in the same season!