Ginny,
To the great ideas given above I want to add another( specially if it's a rainy day :( like happened to us the day we embarked on Voyager in Copenhagen): the Ny Carlsberg Glyptotek museum. It's pretty centrally located, behind Tivoli.
It had works by Rodin and impressionists like Van Gogh, Monet, Renoir, Cezanne and others. Also a lot of greek, roman and egytian art/ sculptures. It's a lovely museum and I was very surprised by how much I liked it.
Don't know what to tell you about the lugagge. Maybe Ngaire knows .