The red-shouldered hawk is a resident at Boomer Lake, and depending on the day/time that I’m up there I will usually see one (even if it’s at a distance). This isn’t an guarantee that I will get a picture of one, but they’re a common sight–sitting on top of posts, the light poles, and within trees (though it is easier to spot them during the winter in the trees, due to no leaves).

Every so often, one will even come to visit the house. Personally, I think it was trying to see what birds were at the bird feeder (easy lunch maybe?).
The red-shouldered hawk is a medium size raptor (basically somewhere in size between a crow and a goose), with broad wings and a medium length tail.
The adults have dark brown and white-checkered wings, and a warm red/brown barring pattern on their chest. The tail is black with narrow white bands.

They’re distinguishable from red-tailed hawks by the barring pattern on their chest (red-tailed hawks have more white), and in flight (where again the red-tailed hawk has more white on the under side of the wings, and the tail is a pale red instead of a bar-pattern that you see for the red-shouldered hawk).

In terms of geographic locations, they are predominately found in the eastern half of the US, though there is a subspecies that is found along the California coast. For those that nest/breed in the northern parts of the US, they will migrate south for the winter. Those found further south, usually are year-round residents.

They’re found in the eastern half of Oklahoma (with Stillwater probably being at west-most edge of the range), and are year-round residents. They have been known to return to their same nesting territory year after year (if they migrate). If they don’t migrate, they continue to stay in the same general area–young moving and finding new territory away from mom and dad.
An interesting little tidbit about young red-shouldered hawks. Once the young reach five days in age, they are then able to shoot their feces over the edge of the nest. So if you know where to look for the nest–if you see a lot of bird poop below, it is probably a sign that there is an active red-shouldered hawk nest above you.

In terms of where you might see them–walking in a forest, but also within city/town parks, near ponds and lakes, basically anywhere there is a small patch of mature trees. Look for a medium size hawk with a nice red-brown barred breast, and you could possibly be looking at a red-shouldered hawk.
Their diet is typical of a raptor: mostly small mammals, amphibians, lizards, and snakes. They will also eat the occasional toad, crayfish, and even other small birds. Though the small birds are usually picked off at backyard bird feeders (and have ranged from sparrows to doves).

While they aren’t currently listed as a threatened or endangered species, they do face threats of habitat loss (clearing of forests) and pesticides (they also had averse dealings with DTT before it was banned, but not to the same degree that other raptors did).
Photography goals: Managing to get a picture of an immature red-shouldered hawk and then also a picture of one catching a meal.
Reference: https://www.allaboutbirds.org/guide/red-shouldered_hawk