OK, so there are a few ways to go here.
One would be to customize the output of the event list widget so that it includes the extra detail you are seeking (please see our Themer’s Guide for some essential background to this). If you are using the widget generally and don’t want it to change everywhere then you could also use appropriate conditions to pull in the extra detail only in certain situations, such as if it is being loaded on the frontpage (or whatever will meet your needs here).
Another could be to take an approach like building your own shortcode then pulling in the next event in a given category via a custom query – that’s possibly a shade more advanced, though.
I hope that gives you a few things to explore here, however we’d really need to leave it to you to hammer out the details of something like this.
Good luck 🙂