Arduino dB meter / noise-level meter - circuit?

The input capacitor 0.001uf is rather small, use 1uF instead. The best diode for that peak detector is schottky or 1N34. The peak detector has a time constant (t=kRC after the diode) where it keeps the voltage peek (you may calculate the t) so if you wait too long the 10uF capacitor discharges through the 2.2k resistor (if no input signal).