For unbalanced signals do you mean tie both the + and - inputs to the signal source, or should one be connected to the source and one to ground?
+in to signal center conductor of unbalanced cable and -in to shield of unbalanced cable.
If using the circuit with a dual PSU, obviously the half-rail biasing is not needed, so R14, R15 and C4 can be discarded, but should R5 be connected to ground or can it be removed as well? (Component numbers taken from http://www.jlmaudio.com/VU%20Buffer%20Circuit.gif)
You can do this "R14, R15 and C4 can be discarded, but should R5 be connected to ground" and remove R9 & R10.
Or only remove R9 & R10 and connect +power rail to +V on VU buffer and -power rail to 0v on VU Buffer with no 0v from the power supply and leave the rails splitting parts.
Main thing to remember is when run this way that the ground plane on the VU buffer is at the -power rail voltage.