I've lived in Leeds all my life. While I don't (and can't easily) think of it as a holiday destination, I don't see why you couldn't have a great city break here. Loads of great ideas on this thread and loads of great places. You won't run out of stuff to do whatever the weather.
Has anyone mentioned Kirkstall Abbey? Depending on DC's levels of interest in historical monuments, it's one of the best preserved abbeys in the country. The Abbey House museum across the road from the abbey itself is also interesting.
Definitely city centre for shopping. Along and off Briggate there's just about every shop you could ask for, nice old fashioned sweet shops and places for a drink and something to eat. Down the arcades there are shops like Yum Yum Beads where you can buy everything you need to make your own jewellery. It's like a pick and mix where you just choose out of a vast range the beads you like and then cords, ear-ring fittings etc to make them into items to wear. The Trinity Centre (also off Briggate) has Superdry, Victoria's Secret, Skechers, Foot Locker, H&M, Top Shop, River Island, Boots, Mango,
Urban Outfitters etc as well as ice cream/pretzel/cupcake etc shops. And a big food court underneath with really interesting stuff.
The art gallery and city museum worth a visit. Museum is pretty hands on.
Betty's in Harrogate is a real treat but a) not cheap and b) involves queuing very often. The ice-cream is to die for though.
While it's not an obvious choice for a break, I think you'll have a great time.