Is there a way to find out which brain surgeon is the best in the country?

No: There are no "best" brain surgeons for every kind of surgery. You would have to be a bit more specific. For instance, there are some brain surgeons who specialize in tumors, some in vascular entities, and some in skull base. If you have a specific type of brain surgery in mind, let me know and i will let you know some national names.

For which problem?: One way of tackling this - look at the brain condition you want treatment for. Given the sub-specialty interests of some surgeons, you may be able to create a list for yourself. This may read something like "best surgeon for brain tumors - mitch berger" "best surgeon for brain avms - robert spetzler" "best surgeon for moyamoya - gary steinberg" etc.