I have one or two thoughts about it.
The hopes are dead easy, the concrete predictions difficult. We have access to a diversity of sound, method and style which has never occurred before. The internet and simple recording technology bring this diversity to the ear in a few minutes. I would hope to see, in consequence, a tremendous liberation of the creative individual musical spirit; a world where every man is, in some sense, his own Beethoven; a world where children were made aware of their right to enjoy and create music after their own fashion, without the odious heft of stress, grind, competition and comparison, which at present leads to a population of a few mentally hidebound successes and a heap of musically inhibited failures.
Specifics ? Soliloquy is right about algorithmic composition. Despite one or two very clever forays, that is still very much in its infancy. Once brains come along capable of melding the two areas of logical and artistic fluency - and I don't think that has quite happened yet, or at least not in precisely the right way - our perception of music will take a quantum leap forward. No way, however, will the personal instrument disappear. Short of our brains actually being wired up to something, the transporting yoga of creating sound while at one with an instrument is here to stay. In particular, I see the future of the piano as being secure for a long time yet.
I think visual notation, that is to say marks on paper approximating sounds, while no doubt carrying on under the economic momentum of centuries, will gradually become less important as a personal means of musical communication; already, a digital piece of music, a computer file, is essentially its own notation. Coupled with a likely upsurge in improvisation as a primary means of musical creation this will imply faster and freer ways than the purely visual of transmitting ideas from one person to another.