Question : How long do most people visit Stockholm?
Answer : Of course you're not most people, but if you were, you'd stay roughly 29 days.
Question : Is there another local airport that can get you to Stockholm?
Answer : Departing from London City Airport is not the only way to get to Stockholm Arlanda Airport. Try searching for flights from London Heathrow Airport (LHR) as well. Over the next two months, flights from LHR to ARN are being booked 14% cheaper than flights from LCY to ARN. Being only 22 miles away, it's easily accessible for most.
Question : Would you be willing to change your travel days if it saved you money?
Answer : Thursday is your cheapest day to fly in the month of June. Flexibility is paramount when booking travel plans in order to keep travel costs down.