Presidents have a number of different resources and institutions that they use to execute their duties as chief of state.
Here's a list of some of them:
- the Cabinet
- the "inner Cabinet" or National Security Council
- the White House staff
- the Executive Office of the President
- the vice president
- the first lady
Which institutional resource is closest to the president?
As for which is closest to him, it would be difficult to argue that any institution can be closer to the President than the 'institution' of the first lady in my opinion.
Very few people have as intimate an access to the president, his thoughts and even his decision making as the first lady.
But a more "textbook" answer would be the following in this order:
the vice president
The White House Staff
Joint Chiefs of Staff