I live in New York and must sue someone in Ohio. Do I need to go to Ohio to do this?

I assume that your promissory note didn't include a chocie of forum provision, in which case it depends on whether New York can exercise jurisdiction over him.  Given that he entered itnot a contract to perform in New York (i.e. to make payments to a New York resident) iit probably can.  Sue him in NY.  However, assuming that you did not include an acceleration provision in your contract (i.e. if you default in any payment, the rest becomes immediately due), you can only sue hom for the amount he owes at that time, however many months' arrears that is.