Out of instruments I could play, I want a nice, vintage, 1940's trombone. That's when jazz was in it's hayday (well in my opinion, that's when all the good music started happening), and they just made stuff better back then. I got to play my band teacher's vintage one day...like holding a piece of history.
But out of ones I can't play, holy crap, upright basses are the gods of strings. Either that or a Stradivarius violin.