We may be in Bern on New Year's Day. Just wondering if any stores or restaurants will be open. Any events happening in that city on that day?

Anyone??

When you say 'anything', do you mean sights, eateries?
Of course the bear park is open, Paul Klee center listed as open, the cathedral can be visited (limited hours as winter).
I think Einsteinhaus is closed. I would imagine all shops closed, but that at least a few restaurants would be serving.
Check www.bern.ch/en for specific info

I would think the bears would be hibernating even if the park is open.

Hmmm...in such an artificial environment, I don't think the staff allow for natural hibernation anyway .

They fight with the bears to stop them from sleeping?

IIRC, the coffee in Switzerland is wonderful. No fighting required. ;-)

Who or what is IIRC?

IIRC = if I recall corectly