Favorite AOII item probably is the daytimer my big made for me (matches my photo album)
Favorite piece of jewelry was (was bc it was stolen) my sister's disk that I was given after initiation. Similar to this:

but with a rose etched on the front and my initials, initiation date, big's initials, and chapter sub-motto engraved on the back. Every sister gets one from her big upon initiation in our chapter.
If I could have any badge I would want one of the fancy historical ones. Preferrably one that you can't purchase anymore.