You can explore Kansas City freely up to a point, but to make any real progress you'll have to visit Sabine and take her Ouija board. It'll let you solve the puzzles associated with each of the other Board of Regents members:
In the tunnels under the Garment District, first squeeze your pendant to see in the dark. Then interpret the Ouija board's clues as compass directions: "SIERRA WHISKEY" is NATO alphabet for SW, "DOT DOT DOT" is Morse code for S; on a clock, "FOUR THIRTY-EIGHT" and "ONE THIRTY" look like semaphore for NE; and the last one says "JUST GO EAST." Talk to Blister to get his vote.
In Sheffield, you'll be stopped in your tracks by a religious advertisement. Head back to the car and go southeast to find your way under the billboard, then cut the wire. Now you can enter Daniel Brume's office. The Ouija board is cluing a word that's eight letters long. When you point at a letter, the board indicates which positions in the answer word that letter occupies. Ask Brume about "TOLOMETH" to get his vote.
In Eighteenth and Vine, first head south to the parking lot and attack the kids. Then enter the castle to play chess with Vykrik. The Ouija board gives a clue for which piece to move at each juncture: "AFTER DUSK" means a knight (it sounds like "night"); "DAWN WITH A NEW BEGINNING" means a pawn (DAWN but with a beginning of P instead of D); "AN E VANISHED FROM ROANOKE" means a rook (delete "ANE" from "ROANOKE"); and "PLAY WENT ODDLY" means a pawn again (the odd letters of PLAY WENT). Now you have Vykrik's vote.
Go to the Financial District, enter the building, and enter the elevator. When you step outside of the elevator, there's a cutscene, and then the game is over. But a question still vexes Lephrea: What is Vykrik's nationality? The main hint is that he's from Prague. The answer to the whole puzzle is CZECH.