I hear you! Much of the hype surrounding Christmas is anything but religious. Come to think of it, few of the people I know who celebrate Christmas do so for obvious religious reasons.
One of the things I love about Judaism is the emphasis on action over belief. In other words, Hanukkah doesn't have to be a religious observance. You can happily indulge in family traditions, and even create new ones for yourself.
There is nothing in the New Testament about decorating pine trees or a jolly man in a red suit handing out presents to children. You can light menorah candles because it's family tradition (even if it's one you're just now starting), and break out the dreidel because the game is fun.
But if you're looking for the "why" behind these activities, that can be an entirely personal journey.
For me, candle-lighting is appropriate in these darker months when daylight can be scarce -- each candle lit (whether for Hanukah, Shabbat or quiet meditation) is a focus for gratitude (that I have candles to light, and that I light and warmth indoors during winter) and is a promise of the return of sunnier days in the spring. Gathering with friends and family is a blessing at any time of year, but in the winter this underscores the necessity of community for survival -- during tough times for Jews and for all human beings.
And latkes.... Well, I just really like potatoes.

This could be a tremendous opportunity to teach your kids about what's really important in life. Is it all the hype and materialism? Do possessions make us happy? Do fancy toys that light up and whirl around make the world a better place?
Or is it the roots that we have through our families, communities and traditions that ground us and keep us anchored as we face life's challenges and embrace life's joys? The winter holidays are an excellent time to remember the benefits to us all through religious and cultural diversity, as well as the strength derived from developing and hooking into our personal cores.
I'm not sure if this is the least bit helpful, or if I'm just running on too little sleep right now.
