Parsing this to mean either law or engineering… If you mean to combine them then the obvious route would be patent law. For general law work at hi-tech firms I don’t think many of the lawyers have an engineering background.
If your friends or parents know some people that are engineers talk to them to get a sense of what the career is like and whether you can really see yourself doing it. Engineering is not like many other majors where you can decide sometime before junior year its what interests you. There are so many required classes that you need to start as a frosh. Nor do those not really committed to it tend to make in thru; the dropout rate nationally for engineering is 50-65%. If you don’t enter college sure that its what you want (although of course you may later change your mind) then I doubt you will get far because the courses are so challenging. This helps your search since you don’t need to restrict yourself to schools with engineering programs.
As for top institutions, they don’t appear likely. Maybe you can get accepted, but top schools don’t have to give away merit money to entice kids to come. Merit money comes from lower-ranked schools that want to tip the scales to bring in strong students that normally would go elsewhere if costs were similar.
One program you should look into is the Western Undergraduate Exchange http://www.wiche.edu/wue which offers close to instate rates at some public colleges in the West. There are rules on major and so on, but if you’d consider a public in another state its worth looking into.