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Often refered to as GM part number 00000000001 (because they seemed to have built the rest of the car around it), it is under the dash, behind the glove box. From under the hood, you can trace the heater hoses on the PS. They pass under the surge tank and into the firewall.
You really don't want to know or ever have to know, but if you do it is inside the passenger side dash comparment next to the firewall. I hope your arms are very very flexible.
i took the car to the dealer to have the heater core replaced. the replaced it, but they reconnedted all the wires incorrectly when they put the car back together. i took the car to Corvette Paramdeics, and they fixed most of the wiring, but there's still one wire in the wrong place, the one that controls the headlights.
So I decided I'm going to try to fix this myself. I need to locate the heater core, and start testing out the wires around it to determine which one is incorrectly plugged in. I took apart the dash. There are a lot of wires down there. So wish me luck...