Open to shorter routes that can be combined with sightseeing/attractions (Castleton comes to mind).
Well, you could always take the bus to Castleton, and then hike Winnats Pass, which is quite beautiful and right outside of town. I loved it there (I actually stayed in Castleton for 5 nights) and really enjoyed the hike although it is steep. If you want something longer, you can continue on to Mam Tor.
There are quite a few hikes in that area, and the Peak website lists some of them here: https://www.peakdistrict.gov.uk/visiting/places-to-visit/trails And here: https://www.peakdistrict.gov.uk/visiting/things-to-do/getactive-walking/peak-district-walking-guides
Another one from Castleton is the hike up to Peveril Castle, which gives you breathtaking views of the Peak District and the chance to explore the castle ruins. Or you could do the 5.5-mile Castleton Circular via Mam Tor, which includes views of Peveril Castle along with places like Cave Dale and the Great Ridge. https://www.alltrails.com/en-gb/trail/england/derbyshire/castleton-mam-tor-circular
I am well aware that Castleton seems to be the centre of the Peak District for this forum.
Castleton may not be in the center geographically, but it is where the hikers congregate. I mostly saw tourists (or locals) in the other towns in The Peak, but in Castleton, I mostly saw hikers; families and solo hikers and many more. There was a lot of camaraderie amongst them. And it's a really charming town, with good options for eating and sleeping. What's not to like? :-)