capital, suburbs of capital
畿 centers on the area around a capital: the capital itself and its surrounding suburbs or metropolitan region.
畿 combines 田 (field) with a phonetic element derived from 幾, which likely contributed the sound and the idea of a boundary or area. The character originally referred to the imperial domain or the region around the capital.
The upper part looks like a complex boundary marker, and 田 inside suggests fields. Picture the capital's outskirts marked by a special boundary enclosing the fields: that's the capital region.
For キ, imagine a key (キー) that unlocks the gate to the capital suburbs: key -> キ, and the key opens the way into the capital area.
Kinki (region around Osaka, Kyoto, Nara)
Kindai University
Kinai (the five provinces in the immediate vicinity of Kyoto)
territories in the vicinity of Kyoto
Kinki Nippon Tetsudō (railway company)
Kinki Nihon Tetsudō (railway company)
the Five Home Provinces (Yamato, Yamashiro, Settsu, Kawachi, and Izumi)
the five home provinces and seven districts of ancient Japan
the Five Home Provinces (Yamato, Yamashiro, Settsu, Kawachi, and Izumi)
Gyeonggi-do (South Korea); Gyeonggi Province
Four Home Provinces (Yamato, Yamashiro, Settsu, and Kawachi; made obsolete in 757)
Kio University
wider Kinki region (Osaka, Kyoto, Nara, Shiga, Wakayama and Fukui prefectures); wider Kansai area
Kinki region (Osaka, Kyoto, Hyogo, Nara, Wakayama, Mie and Shiga prefectures)
Kinki Polytechnical College
Kinki Postal Training Institute