Ok, assuming that DC is like any world capital, 95% of the residents are either working for government or servicing it or servicing and supplying government workers.
That's a crap load of civil servants and hangers on, not to mention lobbyists and lawyers.
Do you really want a whole state made up of people like that?
If it's a new capital though, why not Minot, North Dakota, pretty close to the geographic center when Alaska is added. It's not very scenic but they have an air base and it's two hours away from Regina, Saskatchewan if you want a first run movie. With so little distractions and - 60 temperatures in the winter I bet a whole lot would get done.....