I look at centre as the 3rd defensemen. Cover the front of your net if one of the D-men aren't there. Be the first forward back-checking back. When teams dump the puck in or your team is breaking out, skate back and curl in front of your goal or behind the goal and make it easy for your defense to make the first pass to you.
Going through the neutral zone, I usually advise kids to make smart head-man passes. It's certainly okay to criss-cross the ice to get open or skate with the puck, but make sure all your forwards aren't clogging up the same skating lane.
Anything goes in the offensive zone.

You might be the big-man on the line, so you could set up in front of the net or set up on the half-boards. Anything.