The Drottningholm Palace is on UNESCO's World Heritage list. It is the most well-preserved royal castle built in the in Sweden and at the same time is representative of all European architecture for the period.
In a city full of museums, Hallwylska museet is my favourite. It's also one of the smallest, but you're getting quality over quantity. If you don't have time to go in for proper look, at least stop by for a quick peep of the beautiful courtyard.