How to approach a new data set with no dependent variable
Your assignment is basically the process we call EDA - Explorative Data Analysis.

So what should you do? Simply explore!


What is the shape of your dataset?
How do variables behave, do they have a factor structure, correlate, etc.
What are the main descriptives of your dataset, to they tell an interesting story, etc.


And once you start doing this you will find something that might be interesting to explore a bit deeper depending on your dataset. Do not just use summary functions like mean, median, etc. but also try to build simple graphs and comment everything in a neat notebook!

My tip:

Look at some EDA notebooks on Kaggle for inspiration or watch this superior video by a master at work:

https://www.youtube.com/watch?v=go5Au01Jrvs

Also here is a beginner guide as well:

https://towardsdatascience.com/exploratory-data-analysis-eda-a-practical-guide-and-template-for-structured-data-abfbf3ee3bd9