The Tunnels

Talk to Trevor to start the next quest. Make sure you're healed up and prepared before heading out. Once you're inside the tunnel, start the generator to restore the electricity. Use the pipes to reach the upper door and proceed. You can use your flashlight but remember to turn it off when it's safe to recharge it's battery. You can also use flares to temporarily illuminate the area. You can also do the tasks for Dr. Kessler's sidequest “History Lesson”.

After encountering the first group of walkers, follow the tunnel left to find a dead end. You'll find the Medieval Mod blueprint in the corner, beside the crate.

Return to the intersection and head straight up. You'll find a vault door past the rubble where you need to crouch to pass through. Breach the door in front of the vault door to find a storage room. Kill the enemies inside then loot the items, including the High Voltage Mod inside.

Follow the path around and make your way to the generator room. The door is barred there so you have to find a different route. Jump on the nearby crates and generator to reach the upper part of the room. Jump through the hole and kill the walker on the floor. Grab the fuse and remove the blockade from the door. Replace the fuse in the power box to restore the power in the tunnel.

Exit the generator room and follow the hall. The door that's previously shut due to the lack of power should now be open. Open it and take the ladder down. It is pitch black down here so use your flashlight and flares alternately. Kill the zombies and take a sample from the glowing toxic waste ahead. Next, follow the tunnel to the left to reach a dead-end with the remains of a horribly mutated monster. Grab a sample as well to update Dr. Kessler's sidequest.

There's also the Pride Shotgun Mod blueprint that you can find behind the toxic barrels, by the iron grates.

Follow the path to reach the massive hall with the radar antenna. It will be a challenge to explain the layout of the entire area and it is poorly lit so you'll have to use your flares to illuminate the area ahead of you before moving. The holding cell in the middle of the area has another mod so don't forget to grab it as well.

There's a diary that can be found here as well. Check the left stairs where the radar antenna is pointing and check the collapsed storage cell to find the diary in the shelf.

Exit the storage cell and follow the walkway to the end to reach a room with consoles. The notes for Dr. Kessler's sidequest are found there.

Take the nearby ladder down until you reach the bottom of the hall. Follow the path until the quest is updated.

Continue and clear the intersection. There's only one way here so follow the path to the left to reach the second generator room. Kill the thug inside and loot the fuse from its corpse. Head to the next room and replace the fuse.

Exit the generator room and proceed to the next tunnel. Climb the ladder up to reach the upper level. Grab the rifle nearby and equip it. Take the tunnel to the left and clear the area of smugglers. Open the next door. Grab the ammo nearby and upgrade your preferred firearm. Clear the next area of smugglers.

Once you reached a room with lots of bags, there's a mattress in the corner where an island guide is found.

Examine the vault door however you still need to look for a key for it. Head to the next tunnel and open the door where the Chief Smuggler is hiding. Kill him then grab the key. There's also a Lightning Storm Mod stuck behind the pile of books beside the key holder.

There's also a Secret File on the floor, beside the bed. Exit the room and head to the vault door to exit the tunnels.