What is a word that describes one's satisfaction in the phonetics of a word? Like visual appeal of a pictures, but the audible appeal of a word.
I'm not sure this is entirely germane to your question - whether you're talking about the phonetics as it leaves your mouth or as it hits your ear - but I'll offer "mouthfeel" for the "as it leaves your mouth" part. It is typically used of foods to talk about how it feels in your mouth. (Think of pudding versus crackers versus steak.)
I've never been entirely sure it was appropriate to apply "mouthfeel" to words as well, but I'm not aware of anything else.
Personally, I have loved the "mouthfeel" of the name "Sam" since I was a small child.