I like the full name Adelaide. Somehow it has both oldfashioned femme flourish and practical, immediate tidiness. Ditto Array on the nickname Addie, though - that really is unappealing to me. I might not use a nick at all.
The association I have with the Australian city is pretty strong, but I know nothing about the city itself and I suspect that meeting an Adelaide would lessen that association a lot.
- chazda