When I go back to Zora's Cave, the Queen is gone. I am told that she is out swimming and very late. I went to the lake and swam around but when I came back, but she is still gone. How can I find her?
After completing Hyrule Castle, a number of characters, including the Zora Queen, disappear from Hyrule. This is mostly for flavour and finding where she is isn't a sidequest.
The Zora Queen, like the other disappeared characters, is a Sage and you will rescue her after the Swamp Palace.
She's one of the Seven Sages, so she's in one of the paintings Yuga hid in Lorule. Once you find her painting, she'll be where the sages are, in the Sacred Realm.