We do know that Archer is probably from Utica, or at least not from Albany, given that he's never seen using the phrase "steamed hams" to refer to hamburgers.
Ticonderago is a fine ship name anyway, and the space station in Starship Troopers is also called that. You might want to pass by even if you don't think Archer was born there
Upstate wouldnt have to be a city at all. Could be a town, hamlet village, unincorporated land, state park. Archer was young enough to have been around while earth was still rebuilding in theory.
Upstate itself is also a very general location for the state. It's most commonly used by people from the NYC metro area to refer to pretty much anything north of the bronx. This means upstate could in theory refer to anything from Westchester or Rockland county, to Watertown, to Niagara falls(though dont tell a western new yorker theyre from upstate they'll throw a fit).
His dad was a scientist developing the Warp 5 engine, so I'd guess somewhere which either has a major STEM university or a research lab. Some options would include:
Ithaca- Cornell University
Rochester- Rochester Institute of Technology
Rome- US Air Force Rome Lab
Syracuse - Syracuse University
Those are some pretty solid options. I like the idea of Ithaca. Cornell is a good school. Plus, it would be weird if Captain Archer had a Rochester accent
If you're going to be visiting a potential birthplace for Archer, I'd have to say he grew up in Watkins Glen, if only because the state park there is beautiful
Rick Berman was the executive producer on Enterprise. Given that he was born-and-raised in New York City, it’s possible that the answer is, like, Westchester.