I understand that like any large city you need to always be aware of your surroundings. I also know that there are some areas you best not tread. What areas of Rome that we need to avoid, we are considering a VRBO? Some we were looking at were within a short walk to Termini. I heard that area could be a little sketchy. Thanks

Use normal street smarts and you will be fine. If people approach you offering "help", especially in the train station, firmly send them away. Otherwise, you should have no trouble in the areas surrounding the station.

Termini is fine yes there are annoyances but no real issue, as above be aware of your surroundings, this area has many hotels and tourists so no real problems. I doubt you would find anything in the worst neighbourhoods.

I've stayed around Termini a few times and never had an issue. Note the location is large so distances, especially if with luggage, can be tiring. Unfortunately the distanes seem at the same time too short to bother with a taxi.

Another one saying Termini area is generally ok. If you're hanging around on a street corner at 1 in the morning then you might find it a "bit more interesting" but I've never tried it! I usually stay in the area near Santa Maria Maggiore, generally 2 or 3 times a year. My guess is that some of the suburbs, particularly the high rise ones, are areas to avoid, but in my view somewhere reasinably central should be ok.
As above. .no real problems in the centre.
The only areas that could be dangerous at times are places in the outskirts where no tourists would go.....and they don't have places to stay!
Having said that, Termini is not the place to wave around large amounts of cash or expensive equipment. ...you need to be careful with your gear,esp.at night.

I'd have no issues with Termini either but don't have to stay directly across the street from it. Within a couple of blocks would be fine. As a rule all of central Rome is pretty safe. We've walked quite a lot after dark without any heebie-jeebies. Walking at night is highly recommended, BTW: very nice with lots of people out doing the same and the monuments, fountains and whatnot all lit up!
As lucapal suggested, just keep your goodies (credit cards, cash, passports, smartphones, ipads) where fingers other than your own can't easily get to them but that generally applies to most tourist-magnet cities in Europe. Pickpocketing is somewhat common but violent crime is rare. We haven't lost anything yet, and I know people who've been there many, many times without incident BUT we all take the usual precautions. Light fingers are only interested in easy targets! :O)

One advantage of staying near a train station like Termini is that it's easy to walk to your hotel with your luggage rather than have to hassle with bus, metro or taxi if you're unfamiliar with the city. I like to get to my hotel as quickly and easily as possible and ditch the luggage so I can wander freely. Not a big deal though unless you've got heavy luggage.

OP is from the US, and may be thinking of US cities where some central areas suffer from "urban blight" and tourists could easily wander into "bad" neighborhoods by accident.
European cities aren't like that. They've been around too long and all the central real estate is too expensive.
Think of it this way: don't you figure those centrally located "bad" neighborhoods in the US will get gentrified in, oh, the next 1500 years or so? That's how much of a head start Rome has on US cities.
Yes, you need to keep your wits about you anywhere tourists congregate (train stations for example) because tourists attract predators. But like those in the wild, urban predators are looking for the weakest animals in the herd--targets of opportunity. An ounce of prevention consistently applied is enough to make those predators look for other potential targets.
Have a great time in Rome.