I mean, the absolute cheapest place to put it would be DC if the constraint of not moving the capitol is in place. About 4 million federal employees in the US, DC metro area has about 9 million, so plenty of room, plus most of the federal buildings and offices are right there already. Fairly urban and with a reasonably robust public transport system too. Think you were going for someplace like Kansas, but whatever savings you get on real estate evaporate after you have to take into account cost of transportation to and from DC plus building out the new city’s infrastructure