Sadly, can't recommend an area of Sheffield to live in...
As for airsoft sites, the only ones I really have any experience of are the ones run by Skirmish Airsoft, namely The Stan (Sheffield City Centre), Wentworth CQB (about 30 mins drive into Rotheham) or Skirmish Woodland (about 30 mins drive into Worksop).
The Stan: Very large former Stanley Tools factory set across several levels. Good mix of CQB and a little bit of range, some areas well lit, some almost pitch black. Skirmishing is almost wholly indoors, as weapons can't be fired outside due to access from other people who rent other parts of the site (not too much of an issue to be honest). Some choke points can be fun or really frustrating, depending on your mood, but generally a really good site. Single shot only throughout the venue.
Wentworth CQB: Game days are once a month and numbers are strictly limited. Run across 5 small former accommodation blocks this really is CQB, with engagement distances measured in single digits due to the nature of the buildings. The outside areas are also in play, so there is a great mix of both really close-up and ranged skirmishing. Not really for the faint hearted. As The Stan, single shot only throughout the site.
Skirmish Woodland: Typical established woodland environment shared between paintball and airsoft, with several different 'themed' areas, such as a village, a compound, barricades and a fort. Huge site, which does involved some walking and everything is covered in paint residue from the paintballers. Nice variation in games which are always well paced.
There are several common themes to Skirmish - they employ Marshals that are professional and who actually receive training for their role. They are all friendly and will have a chat with you and are sociable. I have never really seen a marshal go over the top when dealing with a potential issue; problems are dealt with as soon as practicable and without resorting to shouting; I have never seen a marshal attempt to humiliate a player.
The players who attend are normally very sociable as well. Woodland have hire players who sometimes take a whilst to 'come out of their shell' but The Stan and Wentworth don't have hires, and the people who play here are really are sociable - whenever I go skirmishing on my own I always end up chatting with somebody and having a laugh. This can be quite dangerous though, as I have often had to rush to get ready for the next game as I have spent too long talking
There are other sites around Sheffield or fairly nearby, but as I haven't played at these sites it would be unfair to comment about them, but I am sure there are others on here who could recommend other places.