I would be careful about recommending Sheffield. Yes, it is a great city, but it's not for everyone, it's got a very much more grim and less vibrant outlook than many other places even to this day even with changes, but people of all walks of life are nice and you'll get on with them (it's one of the lesser snobby places). It avoids being a city for either very young people or very old people, although it's better being a youngster in some ways than in the past. A lot of outsiders come and live in the much more affluent areas and get a slightly false image of it. Despite the changes outside the university, NHS and council employment sectors there are very few decent job opportunities, certainly compared to some other cities. Shopping wise, sheffield has kept less quality local shops say than places like Leeds or Manchester. A couple of big local shopping areas outside the city centre survived in Sheffield. There is a high concentration of parks/woods/open spaces in some bits of the city, unfairly so which some of the outside invaders can hardly believe. Outside the more affluent areas, transport is difficult, crime is high, there are some no go areas even in broad daylight, especially if you are on foot. There is nothing wrong with living on an estate they are good places where normal people live, but since some of the rebuilding exercises the last few years crime has sky rocketed on some of the estates. It's not so much of a problem if you're mobile.
Cycling wise, a huge proportion of the cyclists live in few small corridors, mostly in the same sector of the city. A lot of people actually cycle in these neighbourhoods. These areas tend to be closer to town, more affluent and flatter than the really big hills than other bits of the city. They tend to cycle very short distances within these neighbourhoods which are pretty pleasant for cycling or make a bolt for the Peak district (as many of them live the right side of town) and rarely cycle anywhere else apart from town. This isn't a complete picture of cycling in and around the city. The road system in Sheffield is a bit weird, unlike some of the graceful slightly curved and wide roads elsewhere in some cities it has roads that weave and split, fork and stop, one way roads, blocked off roads. On the other hand one of the major things that ruins cycling in some cities is a lack of bridges and Sheffield is very well catered for this. In addition there is no proper 'urban motorway' in Sheffield unlike many other cities and apart from the parkway a lack of big bad roads where cycling is banned and hindered. To the west is the Peak district, to the north west are some beautiful valleys such as loxley. To the south are some great fairly untouched valleys outside chesterfield and the fringes of the peak district. To the south east if you put up with a few unpleasant roads you can romp around Nottinghamshire and if you go far enough lincolnshire. For the rest of South Yorkshire a lot of the villages in 'Rotherham' are very nice even though virtually nobody cycles in Rotherham. I could go on and on. Basically if you're not a very nervy cyclist, can put up with a bit of traffic and some hills and learning navigating your way around, have an open mind to explore beyond just the same staple places people cycle, Sheffield is a much better city for cycling than is generally made out.