Park at Bestwood Country Park by Mill Lakes – you’re just off NCN route 6 there. Bestwood’s got a nice bit of gradient and makes for a fun couple of hours blatting around in the woods. Otherwise follow Route 6 up and out (first couple of miles is suburbs) and through Newstead Abbey, Ravenshead, Blidworth to Sherwood Pines. The red is flat but they’ve done quite well with the limited height gain.
I reckon Bestwood > Pines > Red Route > Bestwood is around 30-35 miles or thereabouts.
Otherwise, central notts to the white peak is about 45-50 minutes drive to, say, Ambergate or Matlock…