There's different kinds of Celtic music, too. The fast-paced Irish/Scottish folk music that we'd associate with Hobbits is really pretty recent stuff - but the older Celtic music, like sean nos and violin piobaireachd, has a different tone entirely, and could be seen as Elvish. They're much less...light, I guess? More formal, more deliberate, with a greater sense of age and significance. To me, piobaireachd and sean nos feel more ancient and elemental than other Celtic music, which is how I would imagine Elvish music.
http://www.youtube.com/watch?v=eQy-WjdQPv4
http://www.youtube.com/watch?v=N8paj2hQHIo