What is it about Rice that makes it your dream school? It seems quite different from the rest of your list. If you let us know what it is you love about Rice, then perhaps we can provide other suggestions of schools you might want to consider.
Also, if you can confirm that you have no cost constraints from your parents, that would be great, as it’s a crucial piece to know. Some families who have no financial need are willing and able to pay $80k+/year while others are not. Whatever your family is comfortable doing, members of the board will be able to suggest schools to meet that price point.