I have to agree with Trypsin
music for me is music that moves me or speaks to me in some other way, and it must last, this is just a consequence of what 'good' means to me. Also, this usually means that some fine craftsmanship is involved, to the extent that it the result seems effortless but isn't.
But I don't expect that absolute value judgments on the quality of music are possible.
My expectations of music are very different from someone else's, my taste is shaped by my personality and past musical experiences, things that I may find thrilling or sophisticated may be dull or trivial to the next person.
I have discovered some constants in my own musical taste. Labels (such as musical genres) don't interest me much, because I've found good music in nearly all genres or styles, so I've been trying to find more 'internal' musical features by which to describe my own musical taste and preferences. I'm rather in the dark here, and a degree in musicology would help here as it would provide a terminology and a descriptive framework, but I'm not at all sure to what extent they will actually cover the things I value in music. But some of the things I've discovered are fairly trivial rules, recipes or gimmicks (e.g.: 'use a jumpy bass line against floating high harmonies') and these I'm sure have proper musicological characterizations.
The reason I'm interested in in my own musical taste is simple: music is very important to me. If I could develop some good ways of finding good music without too much effort (having to wade through weeks and weeks of garbage) my life would have more quality. Having some objective measures of my own taste would help here. But it's difficult. I've found that reviews and other descriptions of music, even when they are objective, serious and well-intended, rarely tell me whether the music is worth listening to. And I couldn't mention a single album that is great music all through, even when some of my favourite music is on it.
I'm not ruling out the possibility that an objective description of my own musical taste doesn't exist at all. My reasons for appreciating a piece of music may well depend on other factors than the music itself to such an extent
that apart from a few heuristics nothing sensible can be said about it. If this is true, it is impossible to 'search' for good music, because the quality judgment is formed by how you arrive at it. The jury is still in on this, ladies and gentlemen.