Tips and tricks for visiting beautiful Stockholm?

Hello everyone! This weekend I'm visiting Stockholm and I have some questions. Maybe you are kind enough to help me.

I have two full days and the monday morning to descover your awesome city. So, I want to know what are some beautiful/interesting places to visit but not so many people know about them?

Are there some interesting events this weekend?

And the last one: we are landing at skavsta airport. It is ok if we go by bus to the city centre? We can buy the tickets from there, right?

Have a great evening!