Kolding isn't very big, so getting around in the city centre is quite easy. If you wish to go to more remote locations, e.g. the botanical garden of Geografisk Have, buses are cheap and drive all over town. It should also be possible to get a taxi cheaply (by Danish standards. Taxi-driving is mostly very expensive in Denmark.) As Kolding is not very big, you should somewhat easily be able to get around by foot.