Realistically, a 3.7 (even unweighted) - UIUC won’t happen - and on the top 10 auto engineering list - maybe Iuipui could happen and perhaps Pomona.
All that said, working in the industry, there’s tons of schools that put out automotive engineerings - from a Bama to MTSU to Tennessee Tech - to - really most any ABET accredited MechE program - such as Western Michigan, WVU, and really anywhere. Elon for engineering - ehhhh.
Let’s here more - but honestly, OP can get into lots of schools - but some may require a test - or a test for merit $$.
As they’re looking for smaller schools, here’s a list to look at:
| The University of Alabama in Huntsville | Huntsville | Alabama |
|---|---|---|
| Arkansas Tech University | Russellville | Arkansas |
| University of the Pacific | Stockton | California |
| University of Hartford | West Hartford | Connecticut |
| University of New Haven | West Haven | Connecticut |
| Quinnipiac University | Hamden | Connecticut |
| Florida Institute of Technology | Melbourne | Florida |
| Bradley University | Peoria | Illinois |
| Illinois Institute of Technology | Chicago | Illinois |
| Wentworth Institute of Technology | Boston | Massachusetts |
| Kettering University | Flint | Michigan |
| Michigan Technological University | Houghton | Michigan |
| Missouri University of Science and Technology | Rolla | Missouri |
| University of New Hampshire | Durham | New Hampshire |
| New Mexico Institute of Mining and Technology | Socorro | New Mexico |
| Manhattan University | Riverdale | New York |
| University of Dayton | Dayton | Ohio |
| Shippensburg University | Shippensburg | Pennsylvania |
| Slippery Rock University | Slippery Rock | Pennsylvania |
| York College of Pennsylvania | York | Pennsylvania |
| South Dakota School of Mines and Technology | Rapid City | South Dakota |
| University of Tennessee at Chattanooga | Chattanooga | Tennessee |
| University of Tennessee at Martin | Martin | Tennessee |
| Tennessee Technological University | Cookeville | Tennessee |