The Peak 200 might be a good base for a loop. I'm not familiar with the western side of the outer loop, but I'd probably ride the majority of the rest on my gravel bike (Cotic Escapade with 40mm G-Ones). The only bit I'd not fancy would be Cut Gate, Gores Farm and The Beast (all around Ladybower). You could take the Strines road instead, which is generally quiet for traffic, has great views, and enough steep climbs to avoid any accusations that you've taken the easy option. http://www.selfsupporteduk.net/routes/Peak200.html
Also worth bearing in mind the three major traffic free trails. There are the High Peak and Tissington trails (which are connected) and also the Monsal Trail. Old railway lines, so not the most interesting terrain to ride, but mostly flat, nice surroundings, and potentially a good way to link up different bits of the Peak without having to slog along roads.
Sylwia rode most of the Peak 200 route from Buxton to Glossop (in that direction) on her front-brake only polo-roller. The bananas in her carradice were pretty wrecked by the time we reached hayfield and she ended up a little sunburnt but other than that we were largely unscathed.
The Peak 200 might be a good base for a loop. I'm not familiar with the western side of the outer loop, but I'd probably ride the majority of the rest on my gravel bike (Cotic Escapade with 40mm G-Ones). The only bit I'd not fancy would be Cut Gate, Gores Farm and The Beast (all around Ladybower). You could take the Strines road instead, which is generally quiet for traffic, has great views, and enough steep climbs to avoid any accusations that you've taken the easy option.
http://www.selfsupporteduk.net/routes/Peak200.html
I've also wondered about the South Peak Loop. This is a gentler option, I've thought it would probably make a nice 2 day trip out of Sheffield, with an overnight wild camp somewhere near Carsington water.
http://www.peakhorsepower.co.uk/south-peak-loop/4591186779
http://peakdistrictmtb.org/the-south-peak-loop-is-it-any-good/
Also worth bearing in mind the three major traffic free trails. There are the High Peak and Tissington trails (which are connected) and also the Monsal Trail. Old railway lines, so not the most interesting terrain to ride, but mostly flat, nice surroundings, and potentially a good way to link up different bits of the Peak without having to slog along roads.