"Playing the piano is fun." is much clearer. (Pianos, by themselves, just sit there.)
"The piano is fun." could be used with clarity in these cases:
A: "In your opinion, which instrument is the most fun to play?"
B: "I think the piano is fun." or "The piano is fun."
A: "I know you play both the piano and the trombone, which instrument is the most fun to play?"
B: "The piano is fun. The trombone is hard work!"