I visited Drottningholm in mid-June, and the weather was still quite cold as it was raining. It is easily accessible by bus from the Stockholm city centre, it is closer to the suburb of Bromma.
It is based on Versailles, but is on a smaller scale, of course.
The two main attractions are the Chinese Pavilion (which was a surprise birthday present to Queen Lovisa Ulrika, in 1753!), and the famous 18-century court theatre, where many opera videos and recordings have originated from. The Chinese Pavilion has several beautiful rooms, filled with porcelain, vases and statues. The court theatre, built by Carl Fredrik Adelcrantz, with its pseudo marble, painted fake doors, old thunder machine and wind machine, is a fascinating journey into the opera productions of the early history of the genre.
The palace interior is not very impressive by central European standards, but the lakeside and view of the gardens at the back are stunning. There is also a chapel with a small dome that welcomes a weary traveller after a trek through the vast gardens.
The Palace is included free of charge, on the Stockholm A La Carte pass, issued by Destination Stockholm.