The Tissington Trail and Monsal Trail are both brilliant for easy cycling. If you start the Tissington Trail in Ashbourne, it's uphill very gradually all the way up, then you can easily roll back.
The Monsal Trail is more spectacular and highly recommended, the only problem is that at the Buxton end it stops on a very busy A6, with no way out other than big Hills. So out and back from Bakewell would work well.
Obviously either trail and be supplemented with small lanes alternatives to make circuits; they will all be very hilly though. It's pretty much impossible to cycle on nice roads in the peak without it being a challenging amount of climbing.
Walking, I specifically wouldn't recommend Castleton mentioned above; whilst lovely it is horrendously busy all the time now, and Mam Tor even more so. Alternative suggestions:
- Chee Dale (down by the river alongside the Monsal Trail) is spectacular with stepping stones under the cliffs
- Longnor to Hartington avoids the Dove Dale crowds and is really nice. Dovedale itself is also great, but very busy; all the various side dales are also worthwhile.
- Nearby to Longnor the fossilised reefs of Parkside and Chrome Hill are the only real Peaks in the peak district, and brilliant
- Horseshoe Dale from the bookshop/cafe at Brierlow bar is an absolute delight in spring, carpeted with orchids and very quiet. You can extend down to Dovedale if you want.
- The Dane valley either side of Wincle (nice pub and brewery to sample)
Horeshoe Dale: