I agree with Gator. You should not overlook comprehensive state universities. Your own state’s UTK makes the most sense, as paying for a private engineering education is typically does not provide an advantage. That being said, here are some privates I would investigate:
Clarkson University
U of Rochester
Saint Louis University
Case Western Reserve University
U of San Diego
U of Portland
Vanderbilt University
George Washington University
Rice University
Texas Christian University
As for publics, if they are affordable for you, think about…
U of South Carolina
U of Virginia
Oregon State University
Colorado School of Mines