Can I take my camera to the SA Spurs game?

A Nikon camera, not some cheap small camera.

Sure.
People do it all the time and post their photos and videos on youtube.
Is it a large camera you hang around your neck? I wouldn't suggest bringing one of those.

From the AT&T Center FAQ:

"For Spurs, Rampage, and Silver Stars games, please leave cameras with detachable lenses or lenses longer than three inches at home, along with all video cameras. They are prohibited at AT&T Center events."

Yes, turn off flash though.

Yes. There are thousands of camera users at NBA games. But like what the other guy said, turn flash off to make sure you don't bug anyone.