My favorite part of "New Kid in Town" is the bridge, especially the "there's so many things you should have told her.... but night after night, you're willing to hold her, just hold her, tears on your shoulder...." the poignant vocal, the emotion behind the lyrics and in the delivery, the harmonies, the musical nuances going on... magnificent.
Another thing to think about in terms of what's "underrated" is opinions within the fandom vs. opinions of the general public. I think there are songs like "Too Many Hands" which are underrated by people within the fandom as well as the general public, whereas a song like "Waiting in the Weeds" is underrated by the general public but very highly regarded in the fandom.