I believe "Longmire" is supposed to be somewhere in Eastern Wyoming, near Montana and adjacent to an Indian Reservation
Of course, it is filmed in New Mexico to take advantage of the production tax credits.
I saw a post on the Internet Movie Database (IMDB) that the county the show is based on is Sheridan County, Wyoming. This county has a portion of the Bighorn National Forest in it and its northern boundary is the Montana-Wyoming state line. It is located near the centerline (east-west) portion of the state. There are occasional scenes where the characters travel to Montana in relatively short periods of time, so this mythical Absaroka County is likely on this border as well. There aren't any indian reservations in Sheridan County and the nearest Cheyenne Reservation is northeast of the country in Montana and has 3 or four large counties in between. There aren't any indian reservations in the northern 1/3 portion of the state either. The Absaroka Mountain range is real and forms some of the southeast boundary of Yellowstone National Park. The range is located west of Cody, more accurately southwest of Wapiti, Wyoming. This is in the western portion of the state and not the east. The eastern portion of Wyoming does not have as mountainous terrain as the western portion and I would liken it as high grassland/sage hilly and flatland terrain, without mountains or forests. It resembles much of South Dakota and northern Kansas.
Like much of the show details are vague. I posted on a thread on the IMDB my disappointment with how law enforcement is inaccurately depicted on the show. Some shows are very factual, but sometimes it can detract from the storytelling. In this case the errors are glaring. It appears that the writers and producers have not lived in a rural area at all or at least in a very long time. I'm speaking of remote, rural areas in the west and not the outskirts of Ashville, North Carolina or upstate New York.
One area that is particularly inaccurate is the uniforms of the sheriff and the deputies. Law enforcement officers know that wearing the uniform correctly is needed to project authority and if they don't they are going to have a hard time managing incidents. Law enforcement officers and nearly all firefighters/paramedics have their shirts cleaned and pressed at luandaries. They have a creases place at the midpoint between the sleeves and the buttons and down the center of the sleeves. I lived in small, isolated western counties since 1978 and even in the mid 70's observed deputy sheriff's officers in sparsely populated areas of Idaho, Montana, Wyoming and New Mexico wearing their uniform professionally and properly. The only time I've ever observed a law enforcement officer wearing jeans was 3-4 days out in a National Forest wilderness in central Idaho on horseback returning from the scene of a small aircraft crash. He had to pull the wreckage apart to recover body parts. He rode in with regular uniform pants.
They also show procedures in traffic stops, building entry and handcuffing that would get officers killed, such as, handcuffing prisoners in front as opposed to behind their backs. If that was not enough they show them riding in the back seats of patrol cars not equipped with prisoner transport cages. How quickly can a suspect lift his arms above the driver's seat, place a choke hold on the officer's neck with their cuffed hands and kill the officer? Probably twice in the time it takes to read this sentence.
I wish I could find out where the structure used to depict Walt's home is. It looks like the west or northwest portion of the Valles Caldera and if one was standing on his porch looking out on the meadow it would be in a easterly or slightly southeasterly direction. I have a picture in my mind of a building I've seen somewhere in that area and the red colors strike a bell. It isn't like many of the older structures at Valles Caldera where the logs look like most older, non-maintained cabins do, grey or almost black. I've traveled around a lot of northern New Mexico, but not as extensively as in the southern portion of the state, especially the wonderfully isolated southwest quarter of the state. I've not traveled to the area east of the mountain ranges on the east side of the Rio Grande River valley in the Taos area so "Walt's home" could be in that area. The filming locations listed on the show's IMDB sites are not specific enough to figure this out, and mention Red River and Eagle Nest, places I've not gotten to yet. Red River and Eagle Nest are quite a distance from Valles Caldera.