I love
Cora, especially with this spelling. It's not too common where I live, and is short, sweet and elegant, but also approachable and down-to-earth. If I ever have a little girl, this would be one of the names I would consider.
Corinne is okay, but I prefer
Corinna. It has a little more "je ne sais quoi" for me. This might be because I hear
Corinne more often than
Corinna.
Coral is pretty. I like the meaning. I also like Coraline :)