Kobe Bryant -- Comes Out of Hiding for New Year's Eve With Vanessa

Kobe Bryant made an extremely rare appearance on the Sunset Strip for New Year's Eve -- and he did it with his sometimes estranged wife Vanessa Bryant.

Kobe and Vanessa -- both dressed to the nines -- sure looked like things are back on for 2013 as they walked out of BOA Steakhouse.

We asked the Black Mamba what he's doing to stay on top of his game -- and he answered, "lot of hard work."

Here's the thing -- was he talking about basketball ... or Vanessa?

Her year-old divorce petition is still filed, but our sources say it looks like they're working things out ... again ... for now.