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

One question I had , what has Pike done or going to do that justifies his birthday being a holiday in the 24th century? That's a pretty rare honor which would require something pretty impressive.

It could be a US ship. Perhaps the civilian ships retain their national status and only the military is unified under the United Earth Fleet.