That's a tough one. With only one day, I'd suggest something like this...
https://walksofitaly.com/pompeii-tours/pompeii-tours-from-rome/It says it originates from Rome, but if you're already in the area, you can probably tell them that and have an alternate pick up location.
Whether you use this company or not, I think having a driver will be a huge advantage and make best use of your time.
If you want to do Capri, just plan on making it a most-of-the-day excursion. You could probably fit in Positano or Amalfi, too. But I think it would be tough to do Pompeii and Capri in the same day.