We bought a hardback version of "Twas the Night Before Christmas" for DD's 1st Christmas, and it still gets read every Christmas Eve to her (now 10). I keep that in the "Christmas Eve Box" so it doesn't (a) get lost or (b) get read too early.
The reason for (b) is that we have a large collection of other Christmas books, which has changed over the years but much slower than other books (we had lots and lots of bedtime reading for many years). From December 1st, roughly, we would change from normal books to Christmas and seasonal books for the month.
We also have lots of festive movies (from very young kiddie ones that DD refuses to abandon, to old classics that I love and lots in between). And quite a bit of Christmas music playing on CDs and also Christmas FM and various internet radio stations and DD discovered Spotify last year as well.
I do an advent calendar. DM made a lovely fabric one for DD years ago, and I pop a little chocolate figure into that and something else - like a free printable colouring sheet or a quiz, a note about what we'll do today, and a couple of little toys (one per day not all at once!).
Apart from trying to get my shopping done in lunchhours rather than drag the family on extended treks, I always take 1 afternoon off work and bring DD to "do her shopping". Mostly, it's an excuse for us to look at the "Live Crib" in the city, wander around and enjoy the atmosphere, have a hot chocolate together in a coffee shop and people-watch, maybe getting a few things like her present for DH etc if we haven't already. We try to do that trip on public transport as well, as that adds to the fun.
DD was about to turn 1 for her 1st Christmas (Boxing Day baby!), and was able to stand on a steps at the worktop with me, in her little apron, helping to mix eggs with a fork and roll out and cut out some cookie dough with me. She "made" cookies for crèche every year (in early years, her versions were for home use as there was multiple rolling before baking and they weren't suitable for outside consumption!), and we still do a fair amount of baking together in December.
We also make cookies for Santa every Christmas Eve. I always make sure to do a batch of that dough (different to the other one above) early in December and freeze half, just in case we don't really have time or energy to bake from scratch on Christmas Eve - I can just slice and bake straight from the freezer. But I can distract her if need be with making them herself now.
I think she was 3 before we heard about Christmas Eve boxes. Ours comes out after dinner, some people do them earlier and have activities in them to occupy DCs earlier. But ours is a "lead up to bedtime" type. It contains -
DD's stocking
Plastic Santa plate (gets used in December by DD but Santa gets it on 24th)
Plastic Santa glass (ditto)
Festive hot water bottle
Twas the Night before Christmas
My festive slippersocks
All the above are long standing items and reused every year.
New items are
PJs for everyone (DH, DD and I)
Slippersocks or slippers for DD (usually needs bigger ones)
Lush festive bath bombs (2 - for DD and I), sometimes a festive but manly showergel for DH
Hot chocolate for everyone - the "lump of chocolate on a wooden spoon" type, DH and I sometimes have alcoholic versions
DD then puts out the cookies and milk for Santa, carrot for reindeer and her stocking, before heading up for her festive bath, new PJs, back down for hot choc and a cookie, and then gets her story in bed with cozy HWB to snuggle up to.
We also have tree decorations that we have gathered over the years from holidays around the world. I still try to get 1 new decoration every year (I need about 3 trees now!).
DD used to love various crafting activities in December when smaller - a couple of years, I would give her a shoebox of strips of different coloured paper (mostly plain, a few patterned), and sticky tape pieces, and let her make paper chains to decorate her room, the hall, playroom etc. I also have a few decorations that go up in her room (usually earlier than the tree) and she also has a love of snowglobes so we put up a couple of those in her room as well.
We also do the Irish tradition of the youngest in the house lights the Candle on Christmas Eve - that's DD. We don't do the entire rosary, or even a decade as my DPs used to do, but we do take time as the 3 of us to talk about the year just finishing and the good and bad things to have happened, people to remember etc, and then say 1 prayer together.
I also have my own tradition of taking some time, on a night that DH is out and DD has gone to bed, of turning off all the lights except the tree, usually the fire is lit as well, and sitting/lying on the floor with a drink (sometimes alcoholic but not always), to take some time to myself and contemplate the year, make some plans for the year ahead, remember loved ones who have died or big events during the year like weddings/births, and just make a small oasis of peace for myself in the season. I've done this since I was 16 and babysitting younger siblings (they wanted tv in 1 room so the tree in the other room was quiet and calm).
We didn't usually go to Santa in shopping centres, we went places like the Green Santa in Narnia (Belvedere House in Mullingar) which was cool as DD planted her own Christmas tree to take home and learned a bit about animals hibernating, or on the Santa (steam) train with wandering guitarists and elves as well as Santa making a great family event.
Some of those traditions are new since DD arrived, lots of them were already ones DH and I did, but things evolve over time as well and that is nice too. (I suspect that it won't be long before I can introduce a "stockings for everyone" regime as DD no longer puts hers out for a man in red to fill - the idea being that we'll each put a few bits in the stockings of the other 2).