The Cursed Child is a play based on a story by JK Rowling. It's a sequel to the main Harry Potter story and takes place 19 years later.
I'm surprised you didn't find time to visit Platform 9 3/4. It really exists at Kings Cross station and there's a HP-themed shop next to it.
And Kensington Palace is only home to some of the royal family - most notably the Duke and Duchess of Cambridge (at least until they move to Windsor later this summer). Bits of it are open to the public and are well worth a visit.