Kasen's Hermit World as seen in Antinomy of Common Flowers
Accessible from anywhere
Senkai (仙界, hermit world) is a sealed secret world suited for hermits, which even Gensokyo did not know of before the events of Ten Desires. According to Toyosatomimi no Miko during the first part of a symposium between her, Kanako Yasaka and Byakuren Hijiri, it's a space that Miko had created, herself. A location where nobody else can bother someone is well-suited for hermits.
Geography and People
Little is known about the geography of Senkai. It's accessed via the principle that any crack contains limitless space, which connects the world to any other location allowing it to be accessed from anywhere. For example, Toyosatomimi no Miko showed Reimu Hakurei a way to get to it by pointing to a crack in the ground. Reimu sarcastically replied by asking if Miko was an ant. The residence isn't off-limits to those seeking shelter from youkai, but the hidden nature of the entrance(s) tends to make that option not particularly viable.
Both Reimu and Sanae's endings in Ten Desires which mention Senkai explicitly state that Miko and "her followers"/"the rest" moved to Senkai, and Miko refers to it as "our home" to Reimu. Miko and her followers built a dojo suited for hermits in Senkai after the events of Ten Desires to be their home. This building was described by Reimu Hakurei in the extra stage backstory as pretty big and shiny. It's not yet explicitly confirmed if Senkai is their actual canon action after Ten Desires however, but no other information contradicts it. Symposium of Post-mysticism has Miko describing her current residence as a special location outside of Gensokyo suitable for hermits, which seems to match Senkai's description.
Symposium of Post-mysticism states that Seiga isn't particularly close to Miko and Futo, but does not state if she shares their residence. In page 23 of Forbidden Scrollery Chapter 3, Reimu and Marisa are shown briefly visiting Seiga, Futo, and a third person who is likely Yoshika (from what little you can see of her) in a building, but it is not shown where this location is. There aren't even any pointer-indicators to show where it is on the "map" on the page, unlike the Scarlet Devil Mansion or the Human Village.
Divine Spirit Mausoleum
As of Hopeless Masquerade, Miko has constructed a Taoist temple within Senkai known as the Divine Spirit Mausoleum (神霊廟). It welcomes humans aspiring to become hermits, but most of them fail the necessary training. It shares its name with the area in Stage 6 of Ten Desires, but it is unknown if they are intended to be one and the same.
Kasen Ibaraki's Mansion
Kasen Ibaraki's home lies somewhere deep within the mountain close by the Moriya Shrine, hidden within her own climate-controlled version of Senkai. It is described in Wild and Horned Hermit as being a large mansion by Sanae, though Kasen herself refers to it as a dojo. A scroll with the 8th stage towards enlightenment depicted in Ten Bulls, namely "Both Bull and Self Transcended", can be seen hanging from her wall.
- Ten Desires
In Reimu's ending and Sanae Kochiya's alternate ending, because they were opposed to living in a place under a temple of youkai, Miko and her followers relocated to and built a dojo in another world called "Senkai". Reimu and Sanae Kochiya were invited to it and visited it. In the extra stage backstory, Marisa Kirisame wonders how she can sneak into it.
- Hieda no Akyuu lists Soga no Tojiko's location as "unknown" in Symposium of Post-mysticism.
- Hopeless Masquerade does not explicitly refer to the location as "Senkai" in Futo's ending. However, its description of Miko and Futo's realm as "a space created by hermit arts, it's unclear if it's actually in Gensokyo." is extremely similar to the other descriptions of Senkai.
The Divine Spirit Mausoleum as seen in Urban Legend in Limbo
The Divine Spirit Mausoleum at night as seen in Urban Legend in Limbo