Hi! :)
I don't like the name
Susan particularly, maybe because it's dated, or maybe I just don't like it. However, I don't HATE it. It's a perfectly nice name, it just appeal to me. That said, it's grown on me since I read your post! I actually think it's quite sweet now...
I personally like Susy as a nn, but I'm with you on
Sue. She could always be nicknamed
Annie, but that might be pushing it. I think all nicknames are avoidable; if she always introduces herself as
Susan, then she's less like to get
Sue.