That doesn't exactly make her less suspicious, but Elise isn't terribly inclined to get involved. If the woman is dangerous (which isn't what she's reading off her body language, but she's been wrong before), and what she's remembering is a wanted poster, then an inn is not going to be the best place for her to conceal herself. Pretty much any other option is almost entirely harmless, and Elise doesn't like going around assuming the worst of everyone.

"Sure," she says with a little smile, trying to be friendly, "There's one just down the street, over there." She gestures, and while it's mostly clear where she's pointing, there's quite a crowd so the inn isn't immediately obvious.