I would say the southern Lakes is better than the northern Lakes for walks with a toddler. Walks such as Orrest Head and Gummers Howe are attainable for a 3 year old (perhaps with the help of a carry on the shoulders if he/she gets a little weary). Walks such as around Rydal are also pleasant and achievable.
I live in Kendal which lies on the edge of the Lake District National Park and is also close to the Yorkshire Dales. There's loads to see and do here within easy reach. Walks up to Kendal Castle, lots of cafés, various events taking place at the Brewery Arts Centre, soft play centre, Sizergh Castle (National Trust), Levens Hall, walks around Kentmere, etc. etc. This is also Postman Pat country if you're little one is into that! :)
You have easy access from here to places like the World of Beatrix Potter Attraction, Windermere Lake Cruises, Brockhole, Lakes Aquarium, South Lakes Wild Animal Park, Ducky Park Farm, Lakeside & Haverthwaite Railway, etc. etc.
If you're interested, we have a lovely riverside self-catering place here which sleeps 4, but I don't know when your half term falls and it's already nearly booked up for June. ( www.kendalcottages.com if you'd like to read more).
Wherever you decide, I'm sure you won't be disappointed. I may be a little biased but it is a lovely part of the world. :)