
You can find this bridge by following the mountain to the right. Head away from the door and you will see a bridge above you.
If you didn't get this one during the "Missing Child" Quest, you'll simply go to the Demon Door in Mistpeak Valley. Note: There are 3 entrances to the cavern. The inside area is called the Demon Door retirement home containing a chest, which inside you will find a random legendary weapon. You can either marry your co-op partner in front of the door (requires lover expression pack) or go through all of the different positive expressions until it opens. For this Demon Door you will need a Co-op partner or, of course, a second controller. This Demon Door can be found in the snowy mountain area just up from the Lake. Location: You will find this book when you enter the ticket booth outside of the Mistpeak Monorail Station, it will be on the counter by the cash register. Once here, look over the edge of the cliff to see him on some rocks to the right. Head down from the Demon Door to a spot on the map where a bunch of work equipment is resting (shovels, crates, tables, etc). Head to the Monorail Station and climb up the hill to the right. He's right next to the second silver key you find. He's on top of this door, you can't miss him. Near the Demon Door you will see what looks like a frozen waterfall (it's actually a door). You will exit the cave eventually (should see some ruins), and the gold key will be right there in front of you. Continue along your path, skipping the bridge, and fighting everything you see.
Go towards the frozen lake once inside the cave, and head up the right slope. Enter it through the entrance uphill from the Monorail System (no other entrance will work). You are going to have to go through Chillbreath Caverns to find this gold key.
Face the Monorail Station and head towards the top of the hill to the right.West of the Mercenary Camp's exit, Look for a treasure chest in front of the logs. There is a pile of logs near the Demon Door up the hill a small ways.