Since you asked for the "simplest way", you could just use a LM3914 ( http://www.ti.com/product/LM3914). It's intended use is to drive a VU panel meter but you could just use one output corresponding to level where you want your LED to light.
No.
The LM3914 is a linear voltmeter.
The LM3915 is a logarithmic meter used in audio VU meters.
You need a peak detector that stretches short durations to be at least 30ms for our slow vision to see the peaks.
Thanks audio guru so a lm3915 would be good option?
Regardless of lm3915 or lm3914 you need a peak detection circuit. The lm391x simply takes a voltage input (ie your audio signal) and lights up different LEDs depending on the voltage. If you were to connect your signal directly into the LM391x the led would flash, but because audio is AC you might only get tiny, non-visible flashes of the LED. If you don't need a very sensitive detector then this may work but if you want it to be accurate you want some kind of peak hold.
What you can do is put a diode, capacitor and resistor before the lm391x. This way, when the voltage peaks this voltage is passed onto the capacitor which holds charge and slowly decays. This voltage is then used to trigger the lm391x. Here is a schematic for a design I built using peak detection and an lm3914.
https://github.com/mhollands/Spectrum/blob/master/Schematic.pdfPicture from page three attached. Basically it shows a band pass filter (replace this with a unity gain buffer [Edit] or the amplifier you mention in OP[/Edit]) AC coupled to a diode. The decay of C19 is set by R21 and RV5 (ie how long the hold will occur for). The signal then goes to an LM3914. However if you only have 1 LED you're probably better off just using a single comparator (if you're using a dual op amp for the unity gain buffer then you may as well just use the second opamp as a comparator).
In this case however, the LED will light up for an amount of time proportional to how much the voltage was above your threshold.