I have no experience of Cardiff, but having lived in Manchester for three years as a student, it was fairly decent, especially if you have a car. There are the Clayton Vale trails which are a nice quick loop built in the middle of Eastlands in the city center. They aren't anything too special, but being located in the very middle of the city makes them incredibly accessible for an evening blast. Using a car, there's Lee and Cragg Quarry an hour or so to the north, Llandegla an hour to the West in North Wales and Farmer Johns in Marple. The Peak District is very accessible, especially by train for some natural trails too! Can't go wrong with Manchester!