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This is an intermediary area where you can find the super mutant NPC Marcus and pick up a few quests along the way.
One of the extra things to do is travel to the east side residential area and speak with Seymour the plant. Make sure to have a shovel as he wants to be replanted... and when you do, you'll get xp plus the opportunity for a few games with a sentient scorpion.
Broken Hills Quests & Opportunities:
Here is a list of some of the quests and other opportunities in Broken Hills, each with a brief synopsis containing at least one way to solve it. The remaining ways, and possibly other minor quests I will leave up to you.
1. Fix the mine's air purifier:
Find Zaius next to the mine on the northern end of the residential area of Broken Hills, and consent to find the spare parts to fix the mine's air purifier. You'l have to travel to New Reno (which appears on your world map if it wasn't there already), and find Renesco in the commerical district. Take the air purifier back to the mine, and I'd suggest leaving your party members at the entrance, as you'll be taking quite a bit of damage running through the mine before you get to the end. Zip through the maze as fast as you can, avoiding all confrontations to get to the northeast corner and replace the purifier. When that's done, feel free to engage all the enemies. Return to Zaius for a combat shotgun if you didn't ask for money before.
2. Find the missing people for Marcus:
Talk with Marcus the super mutant and agree to do the favor for him. It's probably best if you complete quest #1 first so that you aren't being damaged in the mine while you complete this quest. It's also recommended for the most xp, to put this quest off until you've completed not only quest #3 but at least #4 and perhaps #5, as Marcus will throw the quest giver of #4 and #5 in jail at the completion of this one.
When you're ready, head into the mine and find the area with the severed bodies. Search them for a letter incriminating Francis. You can then confront him and ask him to leave for xp, which is why you'd want to complete #3 first. Return to Marcus for your reward. As a side note, you can talk to Don in the residential area and tell him you found his wife for a bit of xp as well.
3. Beat Francis at arm wrestling:
For a power fist and some xp, you'll need a Strength of 10 to beat Francis at arm wrestling. Your best bet is to use Buffout until you reach it. Eric's quest at #4 can net you one dose.
4. Divert more electrical power to Eric's home:
Eric is in the bottom row of the residential area. He'll ask you to divert power to his air conditioning. Return to the west side of town to the power station and either talk Brian into diverting the power to Eric, or use Science on the computer in the room for xp. Return to Eric for some Buffout, useful for quest #3.
5. Break Manson and Franc out of jail:
Find Jacob in a building in the eastern end of the west side of town and tell him you either hate mutants or are indifferent. He'll ask that you break his friends from the town jail, just north of Marcus. Go to the jail and if you have a high Charisma (7 or higher), you can talk the guard into giving you a key. Otherwise you can pick the lock on the jail cell door. Your objective is actually only to walk inside and talk to the prisoners, not escape. Walk to the door, save your game, and wait until the guard walks to the southern end of the room. Now pick the door and open it. Speak with the prisoner and you'll be teleported back to Jacob for the next quest and some xp.
6. Blow up the mine's air purifier:
After completing quest #4, Jacob will give you this quest. If you don't care about taking on Marcus as an NPC, or getting the most xp, by all means complete this quest. If you do care about the super mutant or xp, just return to Marcus after you've received this quest and turn Jacob in for some decent xp. Otherwise, run through the mine again, taking damage from the bad air, and use the Jacob gave you on the Air Purifier for almost half the xp you'd have received if you turned them in.