What is your budget? Without this information, recommendations are essentially worthless.
That said, Rose Hulman is a fantastic option for you. You might even get close to a full ride. Very underrated university IMO and focused on undergrad teaching and research. Have you looked at Cooper Union in NYC? Another underrated fabulous school. Clarkson in upstate NY is another good option.
Frankly, applying to OOS to public ivy schools is a waste of time and resources. I would not personally do it. Instead, focus on in your budget private schools.