As a former realtor in New York you have several issues:
1.After receiving your PhD degree, you will either have to sell the house or rent it. You will not be allowed to work in the U.S. without legal documents, so what are your plans if you buy a house in the Rochester area?
2. If you rent the house after you graduate, you will need to pay a Property Management company to keep an eye on it, screen tenants, collect rent, make repairs, etc. Are you willing to pay the fee involved?
3. If you sell the house within 5 years after you buy it, you may not get the full purchase price back and you may owe money on the house. The entire Syracuse-Rochester-Buffalo area does not have the growth potential that New York City and the suburbs have. Upstate New York (Syracuse-Rochester-Buffalo) always had lower incomes, lower economy and suffered during any economic downturn. The area also has a higher unemployment rate than the New York City area does. The State and Local Governments have always "promised" to do something to improve the area but it's always a campaign promise or a photo opportunity. After these politicians get elected, a little happens but not much - just enough for these politicians to claim they did something - which isn't much of anything. The entire region needs a major overhaul.- money wise. Unfortunately, the big money is down in New York City and the millionaires in New York City don't want to spend money in Rochester and they do vote.
4. If you have to sell the house within 5 years, you will owe a foreigners tax, attorney fee, brokerage commission, pro rated property tax and other seller expenses.
5. Mortgage lenders do give mortgages to foreigners BUT you will be required to have a higher down payment + cash for closing costs. The average down payment for foreigners is about 25 - 30% of the purchase price.