The reality is that most of us don’t have a lot of flexibility around our schedules, so inevitably the best time to take photos in Milford Sound is the time that you are there.
If you do have some flexibility, or you are spending more than just a day trip (which is highly recommended) then it's hard to beat the “golden hours”, this refers to the hour after sunrise and the hour before sunset.
Some of the best photos of Milford Sound are taken in adverse weather – striking rainbows streaming out of a waterfall that is flowing sideways because of the wind; shadowy mountains hinting at the landscape beyond through moisture laden mist; and the list goes on.
Start walking! There are so many photos taken from the usual hotspots, so get to a different angle. If it’s low tide head down to the mud flats and get closer to the water; wander the trails and get some great foliage in the foreground framing Mitre Peak; use rivers, creeks and waterfalls as leading lines to add interest to your photos.
Get technical and try some astro-photography. If it’s a clear night, the sky comes alive with the Milky Way and very little light pollution!