1.A binary search tree program that can find certain series of ASCII characters from text files placed in specific directories, and can use these characters to store for future reference in other text files.

2.An x86 "Hello World" type program that runs on a bare machine(obviously, no OS; it's system software).

Which do you think is more "cool" to you?

Option 2.
Because Option 1, once you've got a fully working OS, it's nothing compared to the OS itself.
But Option 2, considering you don't have an OS, is a really cool thing to do.

Option 1 and 2. A binary search program that runs on a bare machine :P