Advice on which parks to visit

Hell everyone! I recently learned that the national park service offers free admission to all 4th graders and my daughter wants to see more parks besides the smokies and Shenandoah which we’ve visited several times previously (we are based in Ohio). Therefore we are going to center our next vacation around seeing more national parks. Our plan is to vacation for 1-2 weeks. What area of the country would you suggest to visit to see a a mixture of the best/as many parks as we can on this trip? While I realize it’s better to spend a longer amount of time in some of the bigger parks, I was thinking 1-2 days at each park given that we may not be out west or south again for a while. Thanks!