@Yourredhead From what I understood they were mostly just making small talk. The prince was basically remarking on the scenery and it's beauty(asking if it's some kind of tourist area or something), and Renee simply agreed that it was indeed beautiful(saying it could indeed be labelled a tourist area). As for the whole "our personal spot" bit she thought to herself, I think she was just trying to find a way to make the experience feel more personal between the two of them to help herself feel better. The prince knows she's having a hard time, and thus he wanted to distract her by making her focus on the scenery more, assuming she wasn't already focused on it.
That's just my take on the situation, mind you.