Funnily enough, I've lived in all of these places! Here's my thoughts:
Aberdeen - I went to uni there and loved it. Pro's: lifestyle, easy reach to beautiful countryside, beach on the door step, lovely relaxed community. Cons: it does get very cold in winter and you are pretty far away from anything else - this can feel a bit cut off (it's a good 2.5 hours to even get to the central belt of Scotland).
Leeds - I lived I'm Harrogate, gorgeous little town; easy reach to Leeds. Pro's: great shopping, nice areas to live in (Headingly, Otley - also, think about Harrogate as the train to Leeds is really easy), nice community, reasonable house prices, gorgeous countryside close by. Cons: seen as far away by people down south so they might not come visit even though it's pretty easy!
Birmingham - I didn't like Brum at all but I moved here alone when I was in my early 20's for work so was quite lonely - this might colour my feedback! Pros - great shopping, house prices are ok, great transport links. Cons - concrete everywhere!, the accent (some people might not mind it but it'd be a factor for me - do you want your kids developing it?), over crowded, I found it very inhospitable (but that could've been me!)
London - again, not my fav. pros - loads of culture, activity, opportunities, all the obvious stuff. Cons : house prices, transport difficulties (traffic everywhere, all the time - Ive been in traffic jams at half two in the morning), everything is expensive - even with London Weighting, you'll still be "poorer".
If it was me, I'd chose Aberdeen (I have ties there and am in Scottish) but if I was you, I'd choose Leeds. It'd probably be the easiest transition from what you currently have and could be lovely.
Good luck., whatever you decide.