First, Rice is an outstanding school for engineering. One of the best in the Southwest, and the best if you’re interested in a smaller school. Second, you also seem to underestimate just how competitive many of the universities on your list are. Remember, even if a school like Rice accepted 14.7% of applicants, that means 85.3% were rejected. Many likely had similar qualifications as you do. The same is true for schools like Princeton EA where 81%, most of whom were almost certainly outstanding applicants, were rejected.
Some other suggestions which are strong academically and may offer merit include Case Western, CU Boulder (super safety), and the University of Rochester. What’s great about CU Boulder and the other engineering school in the Denver metro area, Colorado School of Mines, is that the 2016 expansion of Denver’s public transit system will make it easy to access urban areas on the weekend while still being in a college town environment on the weekdays.