Having been lucky enough to have visited The White House, I was surprised to see that in more recent years that the large tennis courts have now been renovated into a sport court with half tennis and half basketball. They have hosted a few games and tournaments on that very court. So even if you have been there in the past, you might be surprised at the more recent changes and renovations. One of the interesting things we heard about when we were on our tour almost ten years ago was that The White House has a full bowling alley and a movie theater where the president and the first family gets the opportunity to see movies, sometimes before they are released to the general public. I couldn't find it on the virtual map, but I was told it was there. Maybe you can find it?
Go to http://www.whitehouse.gov/about/inside-white-house/interactive-tour and check out the tour. You can also browse their www.whitehouse.gov website for videos on concerts held there, live streams, and podcasts.