Which of these schools are similar or a step-up from our state school?

If he is not sure of his engineering major, schools that are a step up would be those where changing to a different engineering major does not require another competitive admission process (although you may have to apply to the engineering division. Schools where this appears to be the case are listed below (but verify with the schools by contacting directly if the information is not clearly stated on the web site):

Case Western Reserve
Duke
Georgia Tech (only the first major change is without restriction)
Johns Hopkins (except biomedical engineering)
U of Michigan
Northwestern
Notre Dame
Rennsselaer
Rice
U of Rochester
Stevens
Vanderbilt
Washington U

The following (like UT Austin) admit to specific engineering majors, but changing to a different engineering major may require high grades or GPA or be competitive, depending on how popular the new major is relative to the department’s capacity (check web sites and/or contact directly to find out how competitive each major is):

Carnegie Mellon
U of Illinois
Northeastern

The following (like Texas A&M) admit to a pre-engineering status. Admission to a major is dependent on meeting a GPA requirement that may be higher than 2.0 or passing a competitive admission process (check web sites and/or contact directly to find out how competitive each major is):

U of Minnesota
Purdue
U of Washington

The following admits to the major, but has progression requirements that may include technical GPA as high as 3.5 to stay in the major after the first year:

U of Wisconsin