Point Defiance Zoo is great for watching and photographing tigers. If you go at the right time you can find Sumatran tigers in the “Waterfall Panorama” area where they might be lounging, running around or playing in the water. There are no fences or metal meshes to get in the way of photos, and they are close enough to be photographed with 200-300mm lens. You even have a chance of getting a decent shot with the 70mm reach of Sony RX100M3.
Besides tigers there are plenty of other animals to watch or photograph such as the endangered red wolves, clouded leopards or polar bears. They have an aquarium on the same grounds and offer shark dives for a fee. Cloudy days would be best for photographing zoo animals, but on a clear day you can get a great view of Mt. Rainier.
Woodland Park Zoo in Seattle used to have a Sumatran tiger(s) in an open (no fence in the way) exhibit until 2012. In 2015 WPZ opened a Malayan tiger exhibit but the tigers were not in an open exhibit when I visited in 2015. I don’t know if they ever plan on putting them in an open exhibit. Cougar Mountain Zoo has Bengal tigers, but they were also behind a metal mesh fence.
Photography Tip: attending the keeper talks pretty much guarantees that you can see the animals up close and (somewhat) active.