I grew up in South Yorkshire and much prefer it to West Yorkshire where I live now. Your money would go further there, however, your budget wouldn't cover the nice areas. I really don't like West Yorkshire, 1 train an hour, barely a bus service and nothing interesting to do where I live now. In South Yorkshire I had country walks at the end of my road and people were friendly.
I live right on the boundary of S and W Yorks. I'm an incomer of 20 years. I've no pint to prove or axe to grind, but I think that this description, and write off, of W Yorks is a bit unkind and misrepresentative of W Yorks. It's a huge county, with big urban centres - Leeds, Bradford, Halifax, Calderdale, Wakefield, all of which have more than 1 train an hours and are big busy cities with concert halls, museums, shops, theatres, parks, bowling alleys, sports centres, football stadiums, restaurants, even an ice hockey team, indoor and outdoor artificial ski slopes, bike rides etc etc etc ; and glorious countryside - "Summer Wine " country around Holmfirth for example. Some very affluent areas north of Leeds - Wetherby, Otley, Ilkey, and former pit villages around Pontefract which are less wealthy. West Yorks is a very diverse county, you can't just write it off.