Of the 3 sites you mention I've only been to Skirmish, and it's been my regular site since I started playing 4 years ago, really great site. One of the best outdoor sites in the country by my reckoning and the staff and facilities are probably the best I've encountered in my time playing too.
Closer to home, there's Skirmish's other site - Skirmish Airsoft CQB, which is in Rotherham. Though they don't do hire kit unfortunately, it's a pretty hardcore site and I think they worry people might slip or run into something and accidentally break hire guns.
There's also Tac House: Spartan in Chesterfield, again it's an indoor CQB site, they do offer a hire package though, and the site's awesome. One of the best CQB sites I've played. Run by a very experienced bunch of staff who used to run The Stan in Sheffield 2 or 3 years ago, which as it happens is actually being redeveloped by Skirmish, hopefully it'll be open before too long. Probably be early 2015 at the rate they're going at the moment, they've had a lot of set backs. The Stan will be well worth keeping an eye on though, because that probably is the best CQB site I've ever played.
Much closer to home, there's Bawtry Paintball Fields, who on (I think) a fortnightly basis, run airsoft games under BritTac Airsoft. Bawtry is a pretty awesome site and BritTac are very well known, practised airsoft game organisers, they regularly run MilSim events at MoD training facilities, up and down the country.
They're the best 4 sites in the immediate vicinity, but there are some others, Black Dagger in Dronfield and Black Hills in Chesterfield off the top of my head, sure there are more but it's too early for all this thinking lol.