Rye in East Sussex is lovely - cobbled streets (pavements for pushchairs!), antique shops and galleries, cafés, tea shops, restaurants, a couple of miles away from Camber Sands which is an expansive sandy beach, ten miles from Hastings. But again, not in your specified locations...
FWIW, we took C to France on holiday when she was 4 months old and we had a lovely time
