Top end
Of course someone not on a tight budget will be able to stay at the better hotels in Daegu. Readers are cautioned though that what go as deluxe hotels in Daegu are not much better than "motel6".
The nicest hotel in Daegu is probably Hotel the Inter-Burgo, which is far out of the city center.
The next is probably the Walker Lodge, but is only for military.
Others include:
Eldis Regent: drawbacks include small parking lot that is overfilled at any event weddings, usually weekends, but clears out in evening. Also rare for a taxi driver to recognize the name, expect to show a map or give directions from the Prince nearby.
Prince: almost any taxi driver knows when you ask for the Prince Hotel. Parking area seems smaller than the others but generally with less trouble. Standard rooms are fairly large but many seem a bit run down. Water coolers in the hallways save on bottled water. Wireless internet reception varies.
Grand: Rooms roughly the same as the Prince. Has a parking garage but often a tight squeeze.
Daegu Garden: Rooms said to be not as nice as the Prince or Grand, is near a more active nightlife area.
Novotel Daegu City Center: Located in the main downtown area of Daegu, this is the only major international chain hotel in the city of Daegu.