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Guess I'll pitch in seeing no other responses yet. I have not done a lot of photography in this park which I have visited a fair amount over the years.
Old Rag is one of the most popular hikes in the park with great boulders and uphill scrambling but no gear necessary. Sensitive camera gear can go up the fire road to avoid the scrambles.
Somewhat dark skies overhead can produce pleasing milky way images, give it a try.
Big meadow is very pretty. With some nice skies, I'd try that.
You can see black bear, turkeys, and maybe an elusive coyote on your travels. I imagine early am would be a good time for this.
Sunsets from Big Meadow outcroppings (behind or just north/south of the lodge) looking west can give a nice view of the Shenandoah valley.
Although technically not in SNP, Crabtree Falls is just a little to the south and a very popular series of waterfalls.
Most river photos probably are best approached from the bottom of the park, as they are small at the top (clearly). Otherwise, that means a lot of hiking down and up.
If you fly fish, give the Rapidan river a try for native brook trout.