Get the map out and look for anywhere on the Manchester – Sheffield train line. That route is great, it can be used as an emergency bail out option or to get the train out/ride back. About 45 mins from Manc Piccadilly to Edale.
There's the "obvious" trails and routes, the ones that every magazine has done to death or there's loads of local options around Marple/New Mills not too far from Manchester. Buy the Dark Peak Guide Book (Vertebrate Graphics) from the STW shop or a bike shop, that lists loads of dcecent routes with rough timescales and full ride details.