JLR Gaydon is not in the metro area of Birmingham. It's in nice countryside and near a motorway which helps, but it's a fair commute out of Birmingham at rush hour to there. The nice surrounding towns/villages are expensive, and even the shitty ones aren't cheap (hello Banbury) as they're on the edge of commuter distance to London.

Derby I haven't lived in but know people who have. It's an old manufacturing town and hasn't much to offer graduates. Or anyone really. The Peak District is great, and if you can live out that way and commute in then do it. But again, you won't have similar people for local friends.