#daedraologist

One of the main things you can give her is attention. As the goddess of Vanity, if you give her your attention and affection that will count as offering enough.

Other offerings could include perfumes, as her realm is said to be filled with roses. You can also offer silver, as her realm also contains a city made of silver

Another offering could be gems or star iconography to represent her artifact, Azuras Star.

You can also give her keys, as in Kahjiit mythology Azura (or Azurah) is said to have a collection of keys, one of which was stolen by Nocturnal (or Noctra)

You can also offer mirrors to feed her vanity, cat iconography to represent the Kahjiit, moon and star iconography as those are her two main symbols.

As the goddess of magic and prophecy, you can do any kind of divination or spell work in honor of her.