We don't wrap Santa stuff, we set it all up on Christmas eve, ready to be played with upon discovery. That influences which gifts are from Santa at our house.
Likely to be from Santa: Stuff for both kids to share, big or awkward-to-wrap things, toys that require a lot of assembly before play. And stockings.
Likely from us: Books, games, things which are specifically for one or the other child, easily wrapped items, things which might not be played with/used right away.
So, this year, the play tent and the yoga ball were from Santa, and were in the living room waiting to be played with when the kids got up. We wrapped books, a CD player for DS1, a stuffed cow for DS2 who loves cows, some craft supplies, a pizza stone (DH makes pizza with the kids once a week.)