You will be tried and convicted in NY. Your driving privileges will be suspended there (90 days for DWAI, 6 mos for DI) They will notify MN. MN will also suspend your privileges. You will pay a lot of money, need to do whatever NY requires to get reinstated and then do the same in MN. Getting an out of state DUI is a pain in the butt.
It can also make getting hardship licenses during the suspension period difficult.