What verb tense do I use in this question?

It is important that the President live in the White House.

The absence of the expected third personal singular ending s signals the use of the present subjunctive, also called the mandative subjunctive used for states or actions desired, required, necessary, etc. The present subjunctive occurs only in that-clauses, though the relative pronoun may be omitted.

It is imperative that she leave immediately.

His parents suggested he stay a few days longer with his grandfather.

It is called present subjunctive because it is formed from the present tense of the verb, not because it describes events in present time. In the last sentence, the grandfather, parents, and son could be long dead.

When the queen demanded that he march against Ulster, the heart of the insurrection, his army was too weak.

Using the present indicative lacks the sense of should of the subjunctive and only describes a general state or condition.

It is important that the President lives in the White House.

If a state current right now is desired, then use the present progressive:

It is important that the President is living in the White House.