I love Avery Faye! It's a nice name and a sweet way to honor your grandmother. Plus I think Faye is the fresh, new and slightly vintage version of Ray/Rae or May/Mae
I would second the suggestions of:
Charlotte, Blythe, Flora, Catherine, Honor, Georgia, Opal and Margo
Here are a few other suggestions:
Brynn
Brenna
Clara/Claire
Cora/Coral/Cordelia
Cassia
Cecily/Celia/Cecilia
Cleo
Desta
Emmeline
Elinor
Eden/Edan
Eliora
Falon
Isla/Aila
Imogen
Juliet
Jada/Jade
Josephine
Lillia/Lillian
Lilliana
Laurel/Laura
Layla/Lyla
Meredith
Margaret/Marguerite
Penelope
Paige
Priscilla
Pearl
Quinn
Reya
Susannah
Skye
Violet
Winter