I think there are only two c/parks there -- both pretty expensive I have heard
There is a camping ground at silverton but not sure about power
this is worth the time imo
www.travelin.com.au/articles/The-Big-Picture-Broken-Hill-01095
day trip to menindee lakes
you could try this track because I certainly didn't
Not far out to the north east
to the north of the silverton road there's a good size creek with some good river sand to play in --- thinking kids of course haha.
Plenty of little tracks that run off the main roads are worth a drive -- if not fenced/gated I used to poke around them a lot just to see where they went --- a lot are old mine tracks .
Nine mile road -- goes to the living desert state park which is worth a look but a bit over rated --- that road does circle to the north around to silver city h/way -- you can turn right before the stephen creek or cross over the creek and go further nth --- just look for roads (gravel) heading off to the right and that will get you onto the silver city h/way
Just off the black stuff on the nine mile road there was a turn off the left that wondered around the hills -- must be all easy enough as I drove them in the Kia but some would might chicken out

Mundi Mundi lookout: there's a track that drops off to the north from the l/out --- bounced my way down there -- I'm sure the tourist there at the time scratched their heads ---- it runs onto another track and onto another track -- you can't get lost because I didn't
B/H is a good place to wander around but like all places much comes down to local knowledge but many wouldn't know 1/4 the places I found
Eldee Station station has accom + 4x4 driving tracks -- never been there but could be an idea
Things to remember -- big rain or storms can mean flash flooding off that hard country
You can be 10-20 ks out of BH; even see BH, but you can feel and be very isolated
Maybe worth contacting the 4x4 drive club for ideas
Even a drive north along the silver city h/w is ok early am / late pm
The biggest trucks in NSW ; 113 ton AB triples are running to the south on the schw