Size of a non-plated throughole (NPTH) for a spacer
The inside diameter of the spacer is 0.144 inch.  I would make the hole in the board 0.144 inch as well - or big enough to pass the fastener you will be using.

The outside diameter of the spacer is 0.25 inch - if you make the hole in the board that size, the spacer will fall through the board.