I was looking for a YouTube video of the song "Fifty Nifty United States" and found that plus a couple of other things.
Here's the Fifty Nifty song. (lyrics)
Then I found a couple of Animaniacs videos. They are fast and kind of frantic, but fun, and I thought they might still be helpful.
The first is a song of all the states and capitols. (lyrics)
This one is all the nations of the world. (I know this is from several years ago and I haven't checked the accuracy.) (lyrics)
They also had one of the US Presidents, but I found a few things that I felt are objectionable, so we won't be watching that one. (call me old-fashioned, but I don't let my kids use the word "butt")