* Took a solo backpacking trip through Southeast Asia: Most celebrities are known for their glamorous lifestyles and are constantly surrounded by people. It would be surprising to hear one traded all that for a solo adventure through a region like Southeast Asia.
* Worked a minimum wage job for a week: Most celebrities are used to having money and privilege. It would be unexpected to hear they'd choose to experience a week in the shoes of someone with a much different lifestyle.
* Took a class at a local community college: They likely have access to the best education in the world, but taking a class at a local community college would show a real interest in learning for the sake of learning, not for fame or prestige.
* Tried to break a personal record for running a marathon: Many celebrities are athletic, but most focus on maintaining their physical fitness rather than pushing themselves to achieve a difficult goal like breaking a marathon record.
* Started a blog about their passion for birdwatching: Celebrities are often associated with fashion, entertainment, or philanthropy. To find one dedicating time to a hobby like birdwatching and sharing it with the world would be quite surprising.
These are just a few examples. The most surprising thing is really up to the individual celebrity and what we perceive as their typical behavior.