I'd be careful with Binghamton- don't have the exact stats on me currently, but Binghamton is not a nice place & has been progressively getting worse over the years. I actually was just watching a video that said Binghamton was the worst place to live in NY. It's also kind of in the middle of nowhere and the only thing out there is SUNY Bing.
Please see the below link to Binghamton's crime stats. According to this site, Bing is only safer than 4% of U.S Cities. If you are looking for class A or B props, this is not the place.
Binghamton Crime Rates and Statistics - NeighborhoodScout
I'm from the Troy, Albany, Schenectady area & i think it adds a lot more value & there is a lot more opportunity in this area job wise & just in general more to do. There's also a wide variety of A-D properties, so you can find something depending on what exactly you are looking for.
I guess the main point i am trying to make, is don't just jump to the first spot with low prices because you are priced out of NYC, sometimes there's reasons as to why these towns are priced extremely low, so just some food for thought.
If you have any questions about the capital region area, let me know! I am not an agent, lawyer, or lender so have nothing to gain from giving any additional insight.