If you don’t know much about Japanese geography or history, I went and looked up some background information about the places and events in Katanagatari. And some pictures of scenery.
Geography
Japan is currently divided into 47 regions called prefectures. These prefectures replaced the old provinces of Japan in the late 1800s.

A map of the provinces visited in Katanagatari
Here’s some miscellaneous information about the places in Katanagatari:

Cliffs in Kyotango [source]

Tottori Sand Dunes [source]

Izumo Taisha [source]

Kintai Bridge in Iwakuni [source]

Sengan-en, a former residence of the Shimazu clan [source]

Asahidake, the tallest mountain in Hokkaido [source]

Mount Koya, a temple settlement [source]

Shinjuku Gyoen [source]

A random town in Yamagata [source]

Lake Towada [source]

Iga Ueno Castle [source]

Nagoya Castle [source]
History
Katanagatari’s alternate history is pretty similar to Japan’s actual history. For most of its history, Japan had a feudal system where the emperor is technically at the top, but the actual power is held by the shogun, a military leader. There are also lords called daimyo who rule over each province and are loyal to the shogun. All of these positions are hereditary.
Timeline
- (1467-1603) The Sengoku (Warring States) Period– various daimyo fight for control over the country.
- (1590) Toyotomi’s rule- Near the end of the Sengoku Period, Toyotomi Hideyoshi gains control over the country (ruling as a regent instead of a shogun).
- (1588) Sword Hunt (katanagari)– Toyotomi forbids commoners from owning weapons and orders their confiscation.
- (1598) Toyotomi dies. (But not before trying to invade Korea as part of a plan to conquer China.)
- (1600-1868) Tokugawa/Edo period- Tokugawa Ieyasu seizes power and becomes shogun, moving the capital to Edo (now Tokyo). The country is very peaceful and isolationist.
- (1800-1817) Tadataka Inou travels across the country to make the first modern map of Japan. (He died partway, but his team completed it.)
- (1853) Black Ships- U.S. Commodore Matthew Perry arrives with gunships and forces Japan to open itself to Western trade.
- (1868-1912) Meiji Period- After dissatisfied nobles start a civil war, Japan becomes a constitutional monarchy centered around the emperor, and goes through reforms to become more Western and industrialized.
Katanagatari has similar events in its history, but there’s Shogun Kyuu instead of Toyotomi, Shogun Yanari instead of Shogun Tokugawa, and a capitol in Owari instead of Edo. Assuming its historical events happened with the same timing, Katanagatari takes place in the mid 1700s.