Rachel talks about Andrew building her a home "with six columns" and we see the house, named The Hermitage. The house had three main iterations. The first was a simple New England style two-story wood frame home. That was later remodeled with the addition of wings and a wide veranda. The iconic image we have today (and how it still looks) was the third remodeling - but it was done after Rachel's death. Rachel may have involved in the plans for the renovations, but she didn't live to see the finished product.
When Rachel returns to Nashville, escorted back by Andrew Jackson, palm trees can be seen in the foreground. There are no palm trees in Tennessee.