The levels should be just about right if you want 0dB (full scale) to somewhere around full volume. Headphone levels are usually around 1V (at high volumes) depending on the device and the volume level.
But for best results, you'll need to "condition" the AC signal and convert it to varying DC with a peak detector. There are examples in the LM3915 datasheet.
If you want to calibrate 0dB at a lower voltage/volume, you may need an amplifier. Any op-amp will do. It's probably easier to build an amplifier with the "right" gain (which you might have to find experimentally) using a regular an op-amp (just an op-amp and 2 resistors) than with the LM386.