Well, hibernating saves everything you're doing to a session and completely shuts off the machine, so unless you need your computer doing something while you're AFK, hibernating it sounds like the best option.
This is a pretty liberal calculation, but it ignores the power that your monitor, speakers, etc take up. This kind of gives you the idea, though:
Assuming you're using a 350 watt power supply and it's operating at 100% capacity for a full day and electricity is $0.10/kWh, it would cost you...
350 W * (1 kW / 1000 W) * 24h * ($0.10 / 1 kWh) = $0.84/day.
I think that's right, anyway...