It doesn't play music, but you can shell out $2000 for a replica Vulcan lute if you're feeling particularly whimsical.
A somewhat more reasonable $50 will get you a Federation flag to hang on your porch for Federation Day.
This Bajoran earring will set you back $15.
The Star Trek: Original Motion Picture Collection is going for $60 on Amazon. Khan, whales, Kirstie Alley, and all the jazz.
Fill these salt shakers full of sodium ($15) to appease your neighborhood M-113 creature.