I agree with @DadOfJerseyGirl. Make sure your family runs the Net Price Calculator at each school on your list that you’re considering. If the school only offers need-based aid (the Ivies), then if the Expected Family Contribution (EFC) is not affordable, then it should be removed from your list.
Also, make sure that you have at least one (and preferably more than one) school that you would be happy to attend, that your family can afford, and that you are extremely likely to be admitted to. If you need any assistance in creating a balanced college list, let us know. But yes, you certainly have a shot at the most selective/rejective universities in the U.S. Just realize that the vast majority of qualified candidates do not receive an offer of admission.