Here's my suggestions for taking part in this many thousand year tradition:
Clean the house - Well, how about we lower the bar a bit? We could just sweep around the front door entryway and make a big deal about sweeping all of last year's "bad luck" right out the door.
Buy a set of new clothes - I missed out on this when I was a kid. I think this comes from a time when kids might only have had 1 set of clothes that would need replacing each year. But by all means, if they could use a new shirt or pants, this is a great excuse.
Visit close family - The most important part. But if grandparents or uncles, aunts, and cousins live far away, think about a phone call with everyone taking a turn.
Give red envelopes (hong bao) - These are given to the children by the adults. You can buy these at an Asian grocery or make your own out of red paper. Traditionally, you would put money in the hong bao, but you could add a "treat" coupon for a fun activity (bowling, ice skating, flying a kite).
Make a Togetherness Tray - My grandmother would always put one of these out with dried fruits. Here's a way to make your own. Put 4 small bowls in a circle. Cover with a red playsilk, add a cupcake liner into each section and fill with something sweet.
Make a special meal - Kids love helping, especially when there's tasting along the way. Fish or chicken are considered to bring prosperity and long noodles will bring long life. Sometimes, vegetarian dishes are served on New Year's day which may have its roots in Buddhist traditions for self purification.
And now... Gong Xi Fa Cai! (Mandarin) or Gong Hay Fat Choy! (Cantonese). Wishing you prosperity! And may we all prosper in health, in time with our children, and in reaching our dreams.