You will need to wrap your view object with TouchableOpacity or one of the other Touchable components. With TouchableOpacity you have the onPress prop that is passed a press event. From this press event you have access to the x,y coordinates of the press.
pseudo code would look like this:
render() {
....
<TouchableOpacity onPress={(evt) => this.handlePress(evt) }
.... >
<View></View>
</TouchableOpacity>
}
handlePress(evt){
console.log(`x coord = ${evt.nativeEvent.locationX}`);
}