Have one day before our 9 day tour starts in Rome, what should we do or see

We don’t know what sights your tour includes or who you booked your tour with. . Make a list of what’s included and compare to what a guide book recommends to see what you would have missed. Or post a list of what is included in your tour and ask your question again.

Get a good guidebook (Rick Steves Rome will do) and watch some travel DVDs for Rome. And decide what is important for you. You can spend a month in Rome and not hit everything. I know -- we have. Check what is listed for the Steve's Rome tour so that you don't double up. If it is the weekend I would do the Apian Way.

Presumably you are on the Heart of Italy 9 day tour.?

Ostia Antica is a worthwhile use of time and good for a not rushed day, leaving time for a nice dinner back in Rome and a bit of unstructured wandering.

Yes we are doing the Rick Steves Heart of Italy tour. Trying to decide if we should get tickets to Musei Capitolini or one of the other sites in the city

You will not really need tickets to Musei Capitolini. You should be able to just walk up and get tickets. It's an awesome museum and if you can find it, has an awesome terrace restaurant. Last time it had apparently disappeared thru a wormhole to another dimension because I could not find it, hahaha!! Good grief on my part! Is Hotel Sonya the tour hotel? If so it is walkable to Capitoline. I would go via the church San Pietro in Vincoli (St Peter in Chains).

Here is the itinerary for those that don't know:

https://www.ricksteves.com/tours/italy/heart-italy

Will you have data on your phone? IF so I recommend you download Citymapper which makes it very easy to get around on foot!

Is the Borghese Gallery included?
If not do that

Borghese Gallery is a great suggestion. Does the tour include the Vatican Museum? Both are unmissable imho. My personal Rome highlight was simply waking the old center and going into every church along the way. Some have one of kind art, some are just one of a kind, but it’s doubtful your tour will take the time to explore. I’m the evening, head to Trastavere or Testaccio for aperitif, dinner and a stroll. I hear these tours are full, energetic days so would keep the day’s plans conservative.

Take a food tour

"Does the tour include the Vatican Museum?"

Yes, per the itinerary link above the full day in Rome is spent at the Vatican Museums and St Peter's with free time in the afternoon. The morning of the transit day to Volterra is spent at the Colosseum and Forum before the departure.