Depends on which part of London you're moving from, but assuming it's one of the "nice" areas, and you don't want to change your lifestyle/social group too much apart from the weather, then the order to consider them in, probably, would be:
Harrogate (I know that's not on your list but it is very pretty although very, very expensive)
York
Leeds
I've heard both Harrogate and York referred to as "southern towns in the north". (Yes, I know York's a city.) But it really does depend on what you want. Leeds, as someone else said, is a very "edgy" city. Not dissimilar to Bristol but without the same hippy vibe; closer to Manchester with (very) slightly less rain. Whichever one of the three you choose, be prepared for endless conversations about how Yorkshire folk are God's chosen people though and the county is God's chosen back yard.
And don't expect some things to be much cheaper than London, though again, it depends on where you're moving from.
As someone else said, it depends very much what your jobs are too and what you want longer term for your kids. And you will find that just because it looks close on the map doesn't mean it's easy to get to...in many ways getting around in London is easier than trying to commute into/out of anyone of those three (Harrogate slightly less so but not much as it's the smallest of the three), especially if you don't drive. And of the three, if you're not keen on tourists ALL YEAR ROUND (think Bath), then maybe York might not be as utterly picturesque as it seems on the surface. Leeds and York both have good universities though and Leeds has good colleges, from what I recall.