Broken Hills is a mixed community of humans, ghouls and mutants. Like in any mixed communities, there'll be some people who hate other people just because they look different. What else is new?
In the south-west corner, you can enlist as guard for a caravan, if
you still don't know the way to NCR. (Got it back from Vault City,
remember? So no need.) There's also their uranium processing plant.
If you have some uranium ore, you can refine it, and then sell it back
to the city, for some xp. Unfortunately, the only way I've found
uranium ore is from some heavily armed merchants in random (and rare)
encounters in the desert. (Maybe the "Explorer" perk would help, but
other than that, it's a pretty useless perk.)
Talk to Marcus (the super-mutant in the first zone) and get the
assignment to find the missing people. Offer to do it for free. If
you have real good strength, you can wrestle Francis in the pub, and
if you win, you get a power fist as a prize. If you lose, you get
screwed by the mutant and get a ball gag instead :) And, yes, it is
possible to lose even with 10 strength, so save first. (Fun thing to
do is check out the bookcase in his room. He's got a Tandi inflatable
Go east. A ghoul will complain about flies. If you're good at
science, you can go back in the west section and find a building with
a computer on the north side. Use the science skill on it, and
reroute power to the ghoul's house, and optimize the city's power grid
in the process, for good xp. Alternately, you can try to BS the
ghould near that computer, to give Eric more power, but then you
wouldn't get the xp (I think).
Back east, there's a talking plant who wants you to move it elsewhere.
If you have a shovel, do so. The plant will teach you a chess
maneuver. Go find a scientist with a scorpion, talk to the scientist
and ask to test your intelligence against the scorpion. With the
plant's maneuver, you win. And get some xp. The scorpion will attack
you, but personally I always preferred to run and let it live.
Find some sod who'll ask you to find his wife. Find a way into the
underground maze, e.g., through the manhole in a toilet on the south
side. Kill the ants, and find the corpses. Examine all the corpses.
Examine a corpse twice, to find out it's been shot first. Find a
corpse with a letter on it. Take the letter, read it. Go back, find
Francis, and confront him about it. No need killing the poor sod,
btw. Then go tell the sherrif, and the guy with the missing wife. If
you said you'd do it for free, the sherrif will give you a scoped
hunting rifle as a prize. That's a lot more expensive than the 500$
he offered before. (Being generous pays, eh? :)
Back in the eastern section, talk to the super-mutant in the shed near
the mine entrance. He'll ask you to get some components for their
mine's ventilation system, in New Reno, and tell you who to see about
it, and what to say.
So leave for New Reno...