The dwarves in The Hobbit brought their instruments to Bilbo's hole. Did they leave their fiddles, viols, drum, harp, flutes and clarinets there or take them on the whole journey? (I noticed that they did not have instruments in the movie)
There is no further account of them. Considering how large some of the instruments are described, it seems unlikely that they brought them on a trek through the Wild (emphasis mine):
Kili and Fili rushed for their bags and brought back little fiddles; Dori, Nori, and Ori brought out flutes from somewhere inside their coats; Bombur produced a drum from the hall; Bifur and Bofur went out too, and came back with clarinets that they had left among the walking-sticks Dwalin and Balin said: "Excuse me, I left mine in the porch!" "Just bring mine in with you," said Thorin. They came back with viols as big as themselves, and with Thorin’s harp wrapped in a green cloth.
The Hobbit Chapter 1: "An Unexpected Party"
We can be fairly sure that they don't have them by the siege of Erebor; at that time the Dwarves are described as making music using instruments found in Smaug's hoard:
Then the dwarves themselves brought forth harps and instruments regained from the hoard, and made music to soften [Thorins] mood; but their song was not as elvish song, and was much like the song they had sung long before in Bilbo's little hobbit-hole.
The Hobbit Chapter 15: "The Gathering of the Clouds"
There are four likely possibilities for what happened to them:
They left them at Bag-End. Possible, but Bilbo doesn't describe them:
Up jumped Bilbo, and putting on his dressing-gown went into the dining-room. There he saw nobody, but all the signs of a large and hurried breakfast. There was a fearful mess in the room, and piles of unwashed crocks in the kitchen.
The Hobbit Chapter 2: "Roast Mutton"
They left them in Rivendell. Distinctly possible, since it seems to have been part of their plan to rest there. But given the long distrust between the Dwarves and Elves, it seems unlikely.
They were taken by the Goblins under the Misty Mountains. We know that the Goblins went through their packs:
[A]nd there were all the baggages and packages lying broken open, and being rummaged by goblins, and smelt by goblins, and fingered by goblins, and quarreled over by goblins.
The Hobbit Chapter 4: "Over Hill and Under Hill"
And we also know from later that they weren't able to recover most of their luggage:
"I am so dreadfully hungry," groaned Bilbo, who was suddenly aware that he had not had a meal since the night before the night before last. Just think of that for a hobbit! His stomach felt all empty and loose and his legs all wobbly, now that the excitement was over.
"Can't help it," said Gandalf, "unless you like to go back and ask the goblins nicely to let you have your pony back and your luggage."
The Hobbit Chapter 6: "Out of the Frying-Pan into the Fire"
So even if they did bring the instruments as far as that, they almost certainly remained in Goblin Town.
They were lost in Mirkwood. In the extremely unlikely event that their instruments were saved from the Goblins, they were probably either dropped by the Dwarves when they were captured by the Giant Spiders, or else confiscated by the Elves. No mention is made of their luggage through either event, but even if they had held onto their belongings while being trussed up by spiders, it seems unlikely that the Elvenking would have allowed them to keep much, and there was certainly not room in those barrels for Dwalin and Balin's viols.
As Jason's answer points out, the Dwarves were hardly likely to take such large, fragile, and (presumably) precious items with them on such a perilous journey. It seems more likely that they were placed in storage, or perhaps portered back to the dwarven settlement in the Blue Mountains.