Just a quick look at the Internet shows rometoolkit.com which is very useful to give you an idea what to expect and how to get there from Rome. It's 150 miles, so train or bus or even a car with a private driver, its's going to be about three hours each way. Many people prefer Herculaneum.
If this is your first trip to Italy, I know you will fall in love with it and want to go again. I suggest doing q different Tauck tour of Italy next time where you wil be nearer to Herculaneum, arriving two or three days earlier and seeing it then, or staying for longer after the tour but nearer to that destination.
Check Viator.com. They offer tours almost everywhere in the world - just input the nearest city (Naples) or Herculaneum and their offerings will pop up. I looked quickly and see they do a private tour from Rome to Herculaneum that is a little pricey but didn't have time to scroll down to see if there is a more budget friendly option.
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If this is your first trip to Italy, I know you will fall in love with it and want to go again. I suggest doing q different Tauck tour of Italy next time where you wil be nearer to Herculaneum, arriving two or three days earlier and seeing it then, or staying for longer after the tour but nearer to that destination.