What makes an instrument fun to play?
I think that there are a few qualities that make an instrument fun to play. I love instruments that provide some tactile feedback. In other words, anything that allows me to feel my expressiveness is something I enjoy playing. This is part of why I have such a deep love of string instruments: you share a very particular connection to your instrument via the way you color notes with your right hand. By comparison, something like a piano seems incredibly sterile, given that particular consideration. This is also why I have such a huge desire to get to play an ondes Martenot, because you can vibrato the keys themselves! This is also true for wind instruments as the medium by which you create sound is in direct relation to your body: breath.
I also think an instrument that allows you to have a great deal of control over the way a sound is produced is also fun to play. While I do like the particular timbre and idiosyncrasies of playing the harpsichord, (and I even took lessons for it in undergrad!) it just is not as satisfying to play as the instrument that historically followed: the piano. The harpsichord does not allow for varying key velocities and must make dynamic contrasts through adjustments to the manual or couplings of strings. This is a huge limitation to the instrument that makes it somewhat less fun to play, in my opinion.
What makes an instrument fun to experience as an audience member?
I can’t speak for anyone except myself here, but I think things that are visually striking are fun to experience. This is most likely a bad criterion because two performers on the same instrument can be very different (see here and here). (I realize this is sort of an unfair comparison as there is a big difference between high school players and a professional musician, but it serves to illustrate the point.) Audiences like seeing the artist work to bring forth the music, and anything that directly showcases this is something that is fun to watch.
I also think it’s fun to actually feel the physical power of the sound waves. Being in a cathedral when an organist is playing, sitting in the audience during the finale of a Mahler symphony, or even being able to hear a drum and bugle corps in person all have very palpable effects on a listener. This is a big part of what makes an instrument fun for the audience.