Chee Dale, this side of Buxton is well worth a visit, especially if it is a windy day as you are particularly well protected.
Chee Dale is where the River Wye flows through a limestone gorge on its way from Buxton to Bakewell. The Monsal Trail shadows it, so it is accessible to cyclists who want to explore. There are spectacular cliffs which attract climbers.
There is a comprehensive walking route description here: http://walkpeakdistrict.com/chee-dale/
Good car parking.