Does the President have a driver’s license? If so, does he have a Texas or District of Columbia license? I know he probably lost it during the DWI, but he is probably eligible for one now.
The DWI was sufficiently long ago to have made him re-eligible, and I’m fairly sure he has one, since there were images of him driving a vehicle back when he first came to public notice outside Texas.
As for where, he’s a legal resident of Texas – being elected to a public office, even one where a house (White or otherwise) is provided for your use, does not constitute a change of legal residence.
Congressman Bob Etheridge is a legal resident of the small town south of Raleigh from which he hails – and I understand his vote was one of the handful that elected a Town Councilman there in a contested race. Same goes for Senators and such. When my son first moved back to our home town, he lived three blocks from Congressman John McHugh’s home at the time.