The median is an appropriate measure because the data is ordinal, and it represents the middle rating when the scores are ordered.

The mean is the most theoretically sound measure because the difference between a $1$-star and $2$-star rating is guaranteed to represent the exact same increment of quality as the difference between a $4$-star and $5$-star rating.

The mode is appropriate to report because it identifies the most frequently awarded star rating.

Since the data is qualitative/ordinal rather than truly quantitative on an interval scale, calculating the mean assumes equal intervals between categories, which may not hold.