Why not ask yourself what you like most about Cushing, then see if those factors are equally present at other schools? Alternatively, you could list all the aspects that are important to you:
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A boost to law school applications? Not likely, because law schools accept students from a wide variety of backgrounds - political science, psychology, sociology, economics, and so on. Where you attended high school really bears no significance in this equation. The quality of your undergraduate work and your LSAT would matter much more.
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A boost to college applications? While it is somewhat likely that some schools are more readily recognized by college AOs, it would also be more difficult to stand out at those schools. This is definitely something to think about.
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At the end of the day, it comes down to academics/classes offered, activities available, location/size, and the vibe/personality fit at each school. You owe yourself a day at the top 2 schools of your choice.
Enjoy the journey!