I'd take the mountain bike, loads of great rides round there – pretty easy to find off the OS map, and we've had good weather recently, trails are nice.
If you must road bike though, a few ideas, –
A load of stonking good hills but not all on perfectly kept roads (I'd happily ride it on my 23mm tyres) – http://www.gmap-pedometer.com/?r=3537188
Flattish ride for the area (although still probably 500m of climbing over the route) http://www.gmap-pedometer.com/?r=3537173
Good cafes in Wirksworth (french place on the square, or I think there's a bakery too), Cromford (nice but odd veggie café at Scarthin Books, or the greasy spoon at the crossroads),
Each of those is probably about 2 hours each for me, I'm not that serious a road biker, more of a commuter bike pootler, but I am used to riding in hills!
You can extend either by going out and back on the A6 further to the North – the A6 is a great road bike road – fast, smooth, great scenery in parts and if you ride it at a weekend, you are almost guaranteed to find some other road bikers to draft with. Lots of cafes along it too.
Or just a nice ride on the A6 out to Edensor and Bakewell, some nice hills and lots of fast A roads.
http://www.gmap-pedometer.com/?r=3537203
Joe