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
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
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