road-way, street, district, journey, course, moral, teachings
道 centers on a path or way, both literally (a road, street, or journey) and figuratively (a course of action, moral teachings, or a district as a defined route).
road; path; street; lane; passage
Hokkaido (island, prefectural-level administrative unit)
report (of news); reporting; news; information; (media) coverage
road; highway
railroad; railway; rail transport
tool; implement; instrument; utensil; apparatus; device
water supply; water service; waterworks; tap water
orbit; trajectory
prefectures (of Japan); largest administrative divisions of Japan: Tokyo-to, Osaka-fu, Kyoto-fu, Hokkaido and the remaining prefectures
morals; morality
judo
national road; national highway
footpath; walkway; sidewalk; pavement
Shinto; Shintoism
monastery; convent; cloister; abbey
highway (esp. one existing from the Edo period); main road
one-way (trip)
dojo; hall used for martial arts training
purpose; utility; objective
kendo; Japanese martial art using bamboo swords
the way back; the way home; return trip
steady; honest; sober; straightforward; reliable
trajectory; line of fire
distance; journey; itinerary
道 combines 辶 (movement, walking) with 首 (head), suggesting a path that one follows with one's head or direction. The idea of a way or road extends naturally to moral teachings and courses of action.
The movement radical 辶 wraps around 首 (head), like a head leading the way along a path. Think of a road or street that guides your journey, or a moral teaching that shows the right course.
For ドウ, imagine walking down a long road while humming a low 'dough' sound: dough -> ドウ, and the path stretches ahead like unbaked dough.