We usually spend Christmas eve at my mum's house as we are usually home just our little family for Christmas. So, they burn themselves out quite naturally in the furore and excitement of Christmas music, cousins, charades, musical statues, making reindeer food etc.
Then we will sometimes make, sometimes just put out, a special biscuit and glass of milk for FC plus carrot for reindeer, near the tree.
Finally in the evening we make hot chocolate, read a Christmas book and go to bed with a Christmas movie on. I sit with them til they fall asleep.
This year we're actually going to my mum's so I'll be preoccupied with preparing a load of stuff for Christmas dinner at her house. It's actually quite nice because usually I do this on Christmas eve all morning, then by the time we finally get going to mums the kids are quite frantic with excitement, so it will be easier for me to do both things at once and there will be plenty of people there to entertain DC, meaning DP can give me a hand in the kitchen.
We did plan to take them out but quite honestly there is just far too much to do on Christmas eve; I sacrifice a lot of the day time of Christmas eve to make Christmas day more relaxing and enjoyable for myself these days 
We will be taking them out on the 23rd though to the big Christmas display we are fortunate to live right by, then out to dinner at a restaurant. Looking forward to that!