If you've already done Ladybower there's some fabulous walks a bit further on from there. Someone's already mentioned Mam Tor but there's also Padley Gorge just further on from Hathersage in the Hope Valley.
Park at Grindleford train station and head up the gorge, eventually ending up at Toads Mouth. There's a lovely pub at the top, Fox House, for something to eat then head back down the gorge on the opposite side. It's not a massive walk, probably around 2 to 3 hours but it can be a tricky trek with a couple of 9 year olds.
There's also Kinder Scout before you get to Ladybower, there's plenty of parking areas on Snake Pass. If you've not already invested in some, get yourself some OS maps. On the opposite side, the North Peak, there's also loads of walks along Woodhead Pass especially where the Tour de France started out last year.
There's also some fabulous walks round Ribchester, Clitheroe and around the Trough of Bowland.