Bit late to get in anywhere for cheap rates, I fear. Heck I'd go for the Canaries. But that's just me sitting here shivering! Or Cape Verde (am desperate to go there). In reality we are "doing" London: first time we've ever gone there to act like tourists. I would have thought almost anywhere would be an adventure for an 11yo, have you asked what she'd like? Mine actually wants to see Tudor gravestones (strange girl like her mother ).
Cornwall is amazing any time of the year.We stay near Looe,even though it's cold there are so many amazing places to go indoors on rainy days and on dry but cold days there are loads of amazing zoo's,farms,theme parks,museums.
Lots of the attractions provide kennels from around £5 for the day,so you don't have to worry about dogs.
The Moors are lovely in dry weather as well(as long as not foggy)we've found open areas before and gone and flown kites.
We go a couple of times a year and still always find new places to go.
If you fancy going there and want any suggestions for places to visit,I'm happy to help.
I had been looking at PremierInn type places on the outskirts of Paris as I'd need somewhere to park the car. Just got nervous of some of the reviews of dodgy suburbs and walking back from train stations to the hotel.
Have a look at Landal.com. I was just looking at Het Vennenbos here in Holland for someone else - and you can book a 4 night mid week stay from 299 euros of 499 euros for a week. Like Centerparcs but much, much cheaper....