At our house, stockings are not huge: a chocolate orange, candy, and a small gift (This year: gloves for #1Son, socks for DD#1, iPod earphones for DD#2, and a little LEGO set for LilMan). And somehow we've gotten in the habit of adding a toothbrush? lol Anyway, mainly something to keep the little ones busy for a little while and allow the parents a few more minutes sleep! Gifts (wrapped) do go under the tree, except the Santa gift. That is left unwrapped, with the child's stocking next to the gift to make sure it's clear what goes to whom I'd imagine every family does things differently, though.
I love your idea of the stocking by the Santa gifts!
We are a small gathering on Christmas morning. Four adults, one kid, one dog. Everyone has a stocking, mostly filled with cheap trinkets, candy canes, goodies, treats for the K-9. Now that the kiddo is older (almost 11) we usually get up, see Santa gift(s), grab a coffee, hot chocolate or mimosa, unwrap some stuff, eat breakfast, then empty the stockings. But we are open to shifts in the schedule as needed.
I am actually almost ready and looking forward to sitting back and just enjoying the holiday!