Both are great overall and for your specific interest. Both are expensive and difficult to get in. If you want to improve your odds of getting in, ED at Rice would help. EA at HYPSM is almost always a waste unless you are hooked. You may end up not getting in either via RD. Rice has merit scholarships so may become more affordable.
Your parents shouldn’t have to buy a house near Rice, it’s a residential college system with guaranteed dorm for 3 years, majority prefers all four years on campus if they get a spot.
No matter MIT or Rice, living on campus as an undergraduate is part of learning and once a lifetime experience.