In the heart of the downtown core you can find the cultural centre of Stockholm, the Kulturhuset (the House of Culture!).
The House of Culture hosts dozens of contemporary cultural events: photo exhibitions, stories for kids, concerts, films, etc.. It functions during both day and night and houses three cafes and a theater!
If you are traveling with children, make sure to visit Kulturhuset's childrens library! The kids' library has tot-sized tunnels under the bookshelves, and the teen library is strictly off limits for adults! (But it can be a haven for a reading teenager!) It's free, so give it a try.