Thanks for all the suggestions so far!
I should have said, we are local to the area so we've done the "obvious" places like Grizedale and Tarn Hows, so I'm wondering if anyone knew of any other gems. I've previously only really spent my outdoors time being on the hills before having our little one, and so I'm less familiar with the lower ground, and what those paths and trails are like underfoot, and whether they have stiles, etc.
Keep the ideas coming!