Play a Music Disc in Jukebox

You can craft a Jukebox using one diamond and 8 planks of any kind, but the harder part of this goal is getting a music disc to play in it. 

Chests in the Monster Room (Dungeons) can have music discs, 13, cat and otherside. The chance you get at least 1 of these music discs per chest is 38.19%, so if you have a dungeon with both chests that chance jumps to 61.8%. Dungeons can have 0-2 chests, and with a humble sample size of 40 Monster Rooms, the average number of chests I saw per dungeon was 1.575, making your chance of 1 music disc per dungeon 53.09%. 

Dungeons are features that try to generate with at least two sides touching existing cave, meaning they will try to be adjacent to caves, mineshafts, stongholds etc. It is possible for them to be fully buried but only where they take up the whole space of a cave. 

Generic Bastion chests each have a 5.6% chance to contain the Pigstep music disc. This excludes the Lodestone chest in Bridge, the Treasure chests in Treasure, and the outer stables chests in Stables, as those can never have Pigstep. Per Bastion, the chance of getting Pigstep calculated using the average number of chests are:

HOUSING: 43.19% (but jumps to 48.4% if double triple)

STABLES: 36.94% (but jumps to 46.95% if triple triple)

TREASURE: 30.58%

BRIDGE: 20.28% (but jumps to 29.23% if it's double triple)

A ghast killed by a redirected ghast fireball drops the Tears music disc 100% of the time, but the harder part is not letting it fall into lava. This is best done in nether wastes because of the big flat areas, but generally you should be able to force a music disc in the nether this way.

Trial Chambers aren't super consistent for getting music discs. The Precipice music disc is a 4.2% chance from dead end chests, other reward chests, and vaults. Ominous trials are even more unlikely, but if you do get a key your chance for Creator is slightly higher at 7.5%. You can get Creator (Music Box) from pots in Trial Chambers at a 1.4% chance. If you are in a TC anyway, you can bear this in mind to see if you get lucky, but on average you'd need to break 71.4 pots to find it. 

Chicken jockeys are rare, but if you find one, it's a guaranteed music disc as long as you kill the jockey before the chicken. Baby zombies (as well as husks, zombie pigmen etc) can either check for existing chickens (5% chance) or not (95%). If they didn't check, they have a 5% chance of spawning an adult chicken with them. This means each spawned zombie has a 0.24% chance of spawning as a chicken jockey where no chickens are around. If there are chickes in a 10x6x10 cube, the chance increases to 0.49%. 

What does this tell you? Well, don't go out of your way to try to find one. 

WHEN THE GAME UPDATES: Mineshaft minecart chests that generate in sulfur caves have a 42.1% chance to have the Bounce music disc. You can also punch a minecart chest from a mineshaft near a sulfur cave into the biome for this chance, as long as you don't open the minecart chest beforehand. Minecart chests normally can never have music discs.