There are LOTS of options for a photo tour around Anchorage. I think you get the best density of subjects going south from Anchorage, but there are options to the north as well.
Powerline pass from the Glen Alps trailhead (on the hillside above Anchorage) is pretty reliable for moose. Continuing to hike from there up to the Williwaw Lakes is a great hike if you want to do some landscape photography and possibly see some Dall sheep (from a distance).
Taking the Seward highway south out of Anchorage along the Turnagain Arm, you have the chance to see some Dall sheep up close, usually ewes and juveniles. They'll be looking skinny and ratty during the summertime, but they're still a wild sheep. You'll know when/where to look up because any time they're down close to the highway the wildlife watchers will be stopping traffic. Along the way, you'll pass Potter Marsh, just south of Anchorage, which is a popular waterfowl watching/photo spot. Just pull right off the highway for ducks/geese/swans if they're there.
Continuing down the Seward Highway, there are lots of hiking trails around Girdwood. A good option if you're pressed for time and want to see some mountains up close is to ride the tram at the Alyeska Resort. It takes you to the top of the mountain in a few minutes, and from there you are free to hike around. You have a great vantage of the mountains and Turnagain Arm, and can see several glaciers from the top of the resort. You can frame your photos so nobody has to know you paid for the ride up. If you have more time, you can hike the Girdwood end of the historic Crow Pass trail. This gets you right into some very impressive mountains and you have the chance to see Dall sheep or mountain goats here.
The Alaska Wildlife Conservation Center is further down the Seward Highway, toward Portage. They have a lot of interesting critters if you don't mind the high fences. Moose, reindeer, muskox, elk, bison, grizzlies, maybe a few others I'm forgetting.
Just past the conservation center is Portage Valley. There are beautiful hiking trails here, lots of hanging glaciers in the adjacent mountains, and you can take a tour boat ride to the end of Portage Lake to see/photograph the face of the Portage Glacier. You can also get a look at the glacier in the summertime by driving through the tunnel to the Whittier side, and hiking over Portage Pass.
If you end up all the way in Whittier or Seward, you'll have access to the harbors and all the nautical stuff. Boats, sea otters, birds, etc.
Good accessible spots north of Anchorage include Eagle River Nature Center, Hatcher Pass, Matanuska Glacier.