What visual aid or prop would be appropriate for the Romeo and Juliet balcony scene?

Maybe a long scarf or shawl that you can wring, and twirl and weep and moan into.
Sinking to your knees, overcome with greif and weeping into your cloak! lol

Would a mask do the trick? You can enter the scene wearing the mask and when Juliet mentions the possibility of giving up her own name to be with a Montague, she can discard her mask. When Romeo makes himself known, she can rush to put it back upon her face to hide her identity. I think there are a number of staging decisions that can be made with it, and a mask is far less intrusive than clunkier props.

You could have some fun and update it by carrying a cell phone. Texting at the beginning of the scene and staring longingly at it during “wherefore art thou?”

Thank you for all your great ideas! :) I think I may have an idea now.

I was going to suggest a scarf or handkerchief of some type, like @Coloma did. Hope it goes well for you today!