Statistically, if you are already driven to build something, you are likely get more value out of being in a place that is going to maximize your learning potential, exposure to people who can help you mature character, and be recognized by alumni/upper classman/professors who can make a outsized impact in your learning journey.
I would take inspiration from this list and find the smallest, most well capitalized liberal arts school that has quality programs for you to take advantage of. The goal is to find places that have the qualities of the top schools, but where you will be the top 1% where you go, and will be able to maximize the opportunities for learning.
I recommend this even if you are interested in a hard science or computer science field. The benefit for a large majority to establish an educational foundation early on will provide the necessary methods of inquiry to apply breadth or depth based knowledge acquisition in the future.
Instead of seeking out a brand name environment, finding a place where you can mature quickly and confidently learn about yourself will be invaluable for far longer than the brand association to a name brand school.