Interesting! Looks like it's pretty even so far. Although it appears more people from outside the UK say Nye-Oh-Mee, which correlates with my experiences with my little one.
The reason I ask is that I seem to be constantly correcting people (we say it Nay-Oh-Mee), and this is the only way I'd heard it used before. It really surprised me that so many people say Nye-Oh-Mee.
My aunt lives in Australia and she said that over there it is just about always Nye-Oh-Mee.
I don't really mind what people say initially but it does bug me a little when people still pronounce it the wrong way (for us) after being told many, many times NAY!
For those that say NYE, are you in the UK or elsewhere?
Thanks everyone. Keep the votes coming too.