Chicago. Major city, out of range of CSA forces, an important interior transport hub, and plenty of room to build government facilities to boot. Great place to lead a nation from. Not like Washington, I will never understand why they built that city in the first place, especially as tension between North and South was already obvious by the 1790s.
Mark E. said:
I would say Philadelphia. Keep in mind that Illinois and much of the midwest is not yet heavily populated. As for Salt Lake City, it will not be connected by rail until 1869 and Utah is not yet a state.
OOC: Some of the earlier posts have said it's as late as the 1930s. It's at least plausible that Chicago is a major city and transportation center as it more or less was OTL by the 1870s. Especially with no southern route feasible for intercontinental rail, and that would probably get accelerated even over OTL. The Credit Mobilier scandal might very well be swept under the rug or never come to light (with the strategic importance of the thing). I expect Great Northern would pick things up pretty quick, too.