I have an Isadora, and we love the name. We've really only ever had positive comments on it, and people seem to feel it's really unusual so doesn't get filed in the Isabelle/Isabella category.
It's pronounced Iz-a-dora. Only one person (the GP) has ever called her Ice-a-dora, which I'm not keen on!
She doesn't get called Izzy, because we consciously don't call her that as it wasn't the bit of the name we liked. Her nickname is very definitely Dora, and all our friends call her that, as do other toddlers (as it's easier to say than the full name - sounds soooo cute).
I was a bit worried when she was born that it was a bit too 'grandiose' but she wears it really well and no one has ever said anything about it (apart from MN where some people did say it was pretentious...but it's each to their own).
YoungBritish I didn't know about the fear of flying connotation?! The only one I knew of was Isadora Duncan, the somewhat notorious '30s dancer. DH will be less than thrilled if there is another, ahem, wild, Isadora as a namesake!