Edie is a great nickname. She's vintage, spunky, cute, and stylish. If you are looking for something a little longer (but aren't so keen on Edith) here are some choices.
Eda
Edana
Edda
Eden
Edenia
Edina
Edith
Edetta
Edlyn
Edna
Ednisha
Ednita
Edwige
Edwina
Meredith
Mildred
Winifred