https://en.wikipedia.org/wiki/Daegu states that the name of the City means, literally 'large hill' - from 大 (large) and 邱 (hill).
However, the same page also states:
Daegu sits in a basin surrounded by low mountains. Palgongsan to the north, Biseulsan to the south, Waryongsan to the west, and a series of smaller hills in the east. The Geumho River flows along the northern and eastern edges of the city, emptying in the Nakdong River west of the city.
That is also my memory of Daegu - that it is in a valley, rather than being on any particular hill.
Should '大邱' be taken to mean 'large hill', and if so, which large hill is referred to?