I get you about Leeds possibly feeling a bit small. My experience (lived there for 10 years) was that it "punches above its weight": it feels like a bigger city than it actually is.
Pluses: culturally - has an opera house, a good concert season (regular visits by the Halle and BBC Phil, among others), Leeds piano competition, (as you can tell I'm a classical music buff - but certainly when I lived there friends told me the club scene was very vibrant and cutting edge too), West Yorkshire Playhouse (does some really exciting and innovative stuff). It's just under an hour on the train to Manchester, which is a fabulous place, hour and a half to Liverpool (Tate Modern among other things) and half an hour in the other direction to York.
Stuff for children - well, I lived there pre-DC but going back to visit family, there's really good museums like the Royal Armouries.
And the countryside has got to be the one thing you just can't replicate in London. Wharfdale is within cycling distance of north Leeds (as in, cycle out there for an evening after work distance, not major expedition distance). The Dales are beautiful, you have the North York Moors just a bit further away, the Penines to your west, and the Lake District is only an hour and half away. There is nothing even vaguely comparable close to London.
(Having said that, if someone gave me the wherewithall to live in a nice bit of London, well, the cultural life is incomparable, and the amount of stuff to do with children is simply amazing - DC and I try to go there for a long weekend every so often just to do stuff like the science museum, HMS Belfast, the Tower, etc. etc.)