As mentioned Noccundra's good but watch out for the ditch on the left near the shearing shed if you'r going to taxi down from the airstrip to the pub (best off just parking off the strip)...and there's no fuel there either...
Tibooburra's the spot....publican from the Tall pub runs the strip, will come and get you, is a top bloke to boot, has fuel (not much A1 though...), accommodation costs $50/ night and is just a good spot to go. A bonus is there's no dust there atm....it all blew east a while back....
Enjoy