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
2 mile Smithy Beck trail at Ennerdale Water, or a slightly more tricky climb to Bowness Knott viewpoint
Starting from the pay and display car park, walk round the Fish Hotel onto the path towards the lakes. Follow the path and when you get a fork, take the left path which will lead you to the lake. With the lake in front of you, turn right which will then lead you to the base of the Sour Milk Gill falls.
Moss Force is only about a 150 metre walk from the free car park at the top of Newlands Pass to the falls. Take the left fork to go to the bottom cascade and the right fork to head towards the top one.
An easy circular pushchair walk around Tarn Hows with an optional excursion to the waterfalls or Tom Heights