Have you or your parents run the net price calculators for Stanford and other highly ranked universities? The hardest ones to get into will give the best $, which makes more people apply. See if the EFC is affordable. It was just tax time so the financial records should be easy to access. You will also need information such as how much is being put into retirement each year, any home equity, and savings, etc.
Beyond these colleges you will need to balance out your list with places with a higher admit rate and that give full tuition scholarships. There are very few colleges that have a fifteen thousand dollar price tag. However that money can cover your room and board.
The good news is that your scores are high and this is doable.
You are really smart to be looking into this now. It was also really smart of your parents to let you know what is affordable rather than springing it on you later.