We do the same thing that both my husband and I did growing up:
Gifts from everyone except Santa are wrapped and under the tree as soon as they arrive, or are bought (or when the tree goes up for the many things I buy throughout the year). I LOVE the look of those under the tree and enjoy seeing it through the month.
On Christmas Eve we hand out the stacks of gifts and open them up around the tree after dinner (and church if we live near one we go to). We enjoy "having our tree" (as my southern aunts say) at night with the lights on it sparkling. After everything is opened up the kids make a big display of it on dining table and then set out cookies for Santa.
Christmas morning the kids come down to their (one big each--or once in a while a set of a few small items that go together) gifts from Santa set up under (or in front of in the case of many bigger gifts) the tree. Everything is all assembled and put together and set up like a store display (meaning I have spent hours putting together playmobil houses , putting all the people and furnishing in them, adding "magazines" and fake snow around the outside and whatever else to make it look extra special--or whatever the equivelant would be for the year). Stockings will have also been filled with a variety if (unwrapped) gifts. The awe value of the big gift tends to keep the stockings from being thought about for an hour or so though.
We really like how this spreads out the gifts into a longer period of time with more chance to appreciate one thing before moving onto the next--and the kids always love the displays--so the things really look like all those ads make them seem