There are a lot of older homes in the east campus area, and I believe there are some professors that live there as well as students. But the President's house, I think, is south of Hearnes Center, bordering that nature area where the trail goes through.
ETA - I checked this out. The President's Home is known as Providence Point, and it is located to the south of Hearnes, in the wooded area. It is over 12,000 sq ft, 8 bedrooms, and serves both as a private residence and a multi-purpose space for certain events - likely private fundraisers, etc.
There has been discussion about whether the next system president will live there, or if that person will be given a housing allowance and Providence Point converted to a University venue. But it likely wouldn't be torn down.
This post was edited on 6/10 at 6:45 pm