Nora can be found in the second floor of the Inn. At first, if you talk to Nora, there will be a dialogue that will say "Never heard of an Inn raising a cat. Have they been settled before?". After some time, the dialogue will change. The dialogue will say "Good little Nora. You're always at the Inn aren't you?". The second dialogue will mention the Cat's name.
There is one event about Nora where Ann, Doug, Barley, May and Harris meet in the Inn and talking about their food gone missing. When you go to the Kitchen, you can see Nora in the kitchen and will exit the kitchen. When you exit too, you can see them talking about Nora.