The Beatles song "Across The Universe" offers a wide range of possibilities for piano improvisation. The chord progression is gorgeous, and the melody itself has an improvisational-like quality to it.
This video will give you some pianistic ideas to get you started.
Notice how I start with an improvised intro, to establish the musical feel. I also began with an intro to get a little bit away from John Lennon's version. I wanted by arrangement to be pianistic, and express something "in the moment." At the same time, I wanted to be true to the spirit of the original, which I love so much. I enjoyed playing "Across The Universe" so much that I actually didn't want it to end. You can hear this on the video.
I hope you give the song a try yourself. Have fun and see where the music takes you!