Loughrigg Fell is a great little family Wainwright to climb. Easy to navigate from White Moss or the A591 layby.
The Stick Man / Gruffalo trail in Grizedale Forest is fun for the kids and easy too. Follow the Ridding Wood trail signs
Easedale Tarn and Sour Milk Gill from Grasmere is a lovely circular walk of approx 4 miles
Irton Pike, just east of Santon Bridge in the Western Lake District is a fantastic family walk of less than 1.5 miles with stunning views