Question about traveling in the Midlands in England [View all]

I'm planning on visiting the Midlands sometime next month or the beginning of October. Mainly interested in the cathedrals, but also manor houses and museums. I'm thinking of spending a few days in Gloucester and a few in Leicester and using those cities as a base to visit the smaller cities. Should I rent a car or is the train service good? Also, if you have any suggestions of things to see in the area, let me know.