How do you say "show"?
 

I want to say to my friend that when she comes to New Zealand I will show her some of my favourite english bands. "Show" as in, I will let her listen to them. Would I use "misete"? Or is that only for visual things?

That's exclusively used for the visual. You can use it if you're showing her a video or something.

For the audio only, it's 聴かせる.　　

maybe 聞かせる？(kikaseru)

That is exactly what Nagoyankee said, but he used the better of the two kanji for this case. (Obviously... Nagoyankee being Japanese and all :p)

If you are interested in the difference between the kanji I quite like this page:
NHK

It's all in Japanese because, well, why be picky about kanji if you can't read this xD
I think if you aren't sure which kanji to use though 聞 will always be understood.

:)