* She asked where I was going. (This is the most common and direct way to convey the meaning.)
* She inquired about my destination. (This is a more formal way to say it.)
* She wanted to know where I was headed. (This emphasizes her curiosity.)
* She asked me, "Where are you going?" (This is still direct speech, but it can be used when you want to emphasize the question itself.)
The best option will depend on the context of the conversation and the tone you want to convey.