Going to replace my battery today after work. Does anyone know what side it is on in the trunk before I go tearing out everything?

 

Just left of center, over the rear axle.

 

The battery is at the rear of the trunk, on the shelf, slightly to the left.

 

Hee, hee! Tis not as easy or quick as you may expect. The trunk upholstery panels need to come out. The top luggage separator has to come out. The cross brace between the wheel wells must be removed. The side hold-down bracket needs to be loosened. The rear hold down bracket is removed. The assorted wires held back and the battery can be slid back a bit to remove the cables and then the battery can be removed.
Note that this is done while bent over the bumper and reaching way back there. Note that a group 49 battery is no lightweight, don't strain your back.

 

I replaced mine a couple of days ago. In the coupe, you need to remove the back panel in the trunk, the one that has the 4 screws with the plastic heads. The battery clamps loosen easily, but the battery is heavy and awkward to remove. The hold down bracket has to be loosened from below the cross brace. Make sure that you purchase a vented battery that has the vent on the left side as that is where the vent tube is connected. You will need to reset the power windows and the emergency brake after the new battery is connected. The radio presets should be fine so long as you don't leave it disconnected for more that a couple of days.