This is a tricky question to answer as high fidelity audio can be very subjective. You would normally expect that flat frequency response, low distortion and low noise would result in the best audio reproduction, but that isn't always the case. Additionally, opamps with low input bias current tend to be popular for audio to minimize the contribution of current noise especially with high source impedances.
It also depends on the system you are designing? Are you designing a receiver circuit such as a microphone preamp or output circuit such as a headphone driver? Battery powered or line powered?
Here are some of our lowest noise, lowest distortion opamps (in no particular order): AD797, AD8099, ADA4898-1/-2, ADA4899-1, ADA4896-1/-2, AD8597, AD8599.
Not all of those have low input bias current, so many of the following FET input amplifiers would also be good to consider for audio: AD823, ADA4627-1, AD8610/20, AD8065/6, ADA4610-1/-2/-4, ADA4622-2.
For driving heavy loads such as headphones, you'd need an opamp with ample output drive capability such as the AD8397.
Ultimately, you'll have to listen and judge for yourself. Any other feedback or commentary from others is welcomed.
