Last night, we had an appeal play at first while the runner was on second. The pitcher put the ball properly into play, announced his intention to appeal, then threw to first base from the rubber. Is this a balk for throwing to an unoccupied base? Shouldn't the pitcher have stepped off to become a fielder before throwing to first?

It's not a balk when F1 throws to the rubber for the purposes of making a play. That's what he did here -- for the purposes of making an appeal play.

IT's legal.

Decisions. Decisions
 

So did you call him out or send him to third?

No reason for a balk call. Honor the appeal and make your call.