You want to be on top of the hill. FYI-the area south of Mercer St is not Lower Queen Anne (like some people call it) it's called Uptown. Technically Lower Queen Anne would circle the whole perimeter. If you're not on the hill you're not on Queen Anne Hill. Frankly, some Queen Anne residents don't consider anything east of Aurora Ave N/HWY 99 or anything south of Mercer St, Queen Anne hill either. The "boundaries" have been stretched out due to Real Estate Agents and Developers trying to create an image for marketing purposes.
You did not mention the age of your children? If you're going to let them ride a bike in this area (EAST QA) I'd say NO due to all the traffic from the aforementioned arterials. Also there are no parks and playgrounds WITHIN WALKING distance for children. If you love your children, you want to stay west of Aurora Ave N/HWY 99.