Schools I have shot of getting into?

I am from Ohio and am looking to do engineering in college. As of now I have taken sat twice and gotten 1890 and 1840 (both times I achieved 1200 math/reading). The 1890 has a lower math score so I guess my best score would be the 1840. I am taking the SAT again in October and hope to get a 2000. ( I took the June SAT that had the mistake which cost me a significant number of points). I have a 4.0 GPA (91.00%) at one of the best high schools in the nation. I took precalc junior year and will ttake AB AP calc senior year. I’ve done track/cross country first 3 years and was varsity (we were #23 in nation) my junior year however I hurt my ankle and will be the manager this yea) I did service my junior year every week and will do some clubs senior year. My top choice right now would be the Univ of cincinnati mainly becuase of their Co-op program. I’m interested in their Architectural (1270avg SAT) and mechanical (1310avg). They say they empazsize math the most though. Other schools I’m considering are:

Cincinnati (legacy - dad)
Ohio state (legacy mom)
Lafayette college (legacy - grandpa- semi famous aero engineer)
Pitt
penn state
nc state
purdue
miami ohio
miami Fl (longshot)
Southern Cal ( long shot)

Could someone knowledgeable assess my chances at these schools and maybe tell me some other schools I should consider? Thanks so much

Cincinatti- no idea low match/ safety???
OSU- safety
Lafayette- Low reach (SAT score is low) bump it up 60- 100 points for match
Pitt- Match
PSU- match
Purdue- low reach (engineering is competitive there)
Miami Ohio-???Match???
Miami Florida- Low reach, they don’t have good engineering anyways idk why you would want to go there. Great school but terrible engineering
USC- sorry no chance

I disagree with MegaMetalHead’s assessments. Ohio State (engineering) is not a safety for you, but a reach. Ohio State does not consider legacy status. Your 1200 SAT (M + CR) is low, and is equivalent to a 26 ACT, which is the bottom 25% of admitted applicants, and likely even lower for admitted applicants for engineering. You need to boost your SAT score. Or try the ACT in Sept or November. I don’t understand how a 4.0 gpa equates with a 91 average, as 91 seems a bit low, esp. for engineering. Your extracurricular varsity track is good, but if thats the only extracurricular you were involved with, that is not be enough to compensate for the low SAT and gpa. I don’t see any of the schools you listed as a match for you, except maybe North Carolina State and Miami of Ohio, because you seek one of the most competitive majors (engineering) and your 1200 SAT puts you at or under the bottom 25% of admitted applicants for all the other schools you listed. You need to find some more safety schools for engineering. I don’t know if Lafayette considers grandparents as legacies. If so it may help you there. Your SAT score is just above Lafayette’s 25% mark (1180-1370 is mid range–25% to 75%) of admitted applicants, but that is of all applicants, engineering would be lower.