Microchip dsPIC33 audio DAC: has anyone succeded using it without noise?
Quick review:

Hypothesis: noise on AVDD.

LC ringing? If you want to do some passive lowpass filtering, and use separate regulators for analog and digital, the place to do it is before the regulator. L1 will create a LC circuit with C2 which may resonate and create lots of noise on AVDD. This depends on the ESR of L1 and the ESR of both caps on each side of L1. If checking with a scope reveals ringing on AVDD, then L1 is the problem.

Unstable LDO? AP1117 datasheet says "When using
Aluminum electrolytic it is still recommended to also use a 1µF MLCC in parallel." Here we have 100nF only. Regulator may be marginally stable or ring.

Fix for previous 2 issues: replace L1 with wire. Remove C12 (redundant, we have C2 already). Replace C2 with largest value ceramic that will fit, at least 1µF according to AP1117 datasheet. Check ESR of 100µF cap in capacitor datasheet, compare with LDO requirements.

If you want to check if your LDO is stable, connect the output to a function generator, square wave, 0-3.3V, via a resistor of say about 100 ohms. This will cause a current of 0-33mA to flow and you will see the regulator's step response on the scope. Compare to step responses in datasheet, which are clean. If it wiggles or rings then you have a problem.

1.65V should be AVDD divided by two, not the presumably noisy input voltage going through a divider.

MCP6002 works on 5V max, schematic shows +9V supply.

Layout: 


  Here is the layout (bottom layer). The top layer is a GND plane.


There are cutouts in the ground polygon pours on bottom layer, are there also cutouts on toplayer or is it a continuous ground plane?