For a STEM degree a “step up”… CMU, GaTech, Hopkins. He’ll need a 1500 SAT for these.
RPI is a “step up”, but they are lesser known.
The same level as UT… Washington, Michigan, UIUC
Step down… Minn, Purdue, CASE, Wisconsin
For a nice university environment with UT level STEM… Rice, Duke, NW. Rice is too small though.
Expensive privates… Northeastern, Washington U, Vanderbilt, Notre Dame… for STEM these are a step down.
I don’t know enough about Stevens & Rochester to comment on them.