Today, our environment and the objects therein are equipped with an increasing number of devices such as cameras, sensors, and actuators, which all together produce a huge amount of data. Furthermore, we observe that citizens generate data via social media applications running on their personal devices. Smart cities and societies are seeking for ways to exploit these vast amounts of data. In this paper, we argue that to take full advantage of these data, it is necessary to set up data governance properly, which includes defining, assigning, and allocating responsibilities. A proper setting up of data governance appears to be a challenging task since the data may be used irresponsibly, thoughtlessly and maliciously, resulting in many (un)wanted side effects such as violation of rules and regulations, human rights, ethical principles as well as privacy and security requirements. We elaborate on the key functionalities that should be included in the governance of a data ecosystem within smart cites, namely provisioning the required data quality and establishing trust, as well as a few organizational aspects that are necessary to support such a data governance. Realizing these data governance functionalities, among others, asks for making trade-offs among contending values. We provide a few solution directions for realizing these data governance functionalities and making trade-offs among them.