We are flying into Providence for a business trip in Boston. We're going to spend some time on the Cape. Should we schedule any time to spend in Providence? We'll have our 3 kids under 8. Is there anything beside gorgeous scenery in Providence?

Federal Hill has some great restaurants. AND Providence has spent some big bucks recently renovating their "Riverwalk" area. There are barge processions and lights and lots of shops. It is beautiful - you may want to check the city of Providence website for better detailed info on that!
Providence can be worth a day or so, depending on what you are looking for - perhaps an evening before and a day before heading out to the Cape.

Can you get over to Newport? Lots of shops, Cliff Walk, beaches, and of course the mansions. The kids would be a bit young for the tours, but perhaps you and your spouse could trade off watching the younger kids outside, while the other tours inside with the oldest.

I agree with Beth. Providence is a great little city, but if you want to spend one single day or even just an afternoon in Rhode Island, Newport is the place you want to go. And as a native Rhode Islander, I'm puzzled by the use of "gorgeous scenery" and "Providence" in the same sentence. I mean, Providence isn't ugly and dirty, but gorgeous? Someone has seriously been pulling your leg.

Providence is "gorgeous". I have never seen a city or a shopping Mall as beautiful as the one in Providence. We went to Raphaels for dinner last week. I was in awe on how beautiful the city looked at night. We had guest from Sweden with us who are world travelers, and they remarked on the beauty of the city.
Roger Williams Zoo has a baby polar bear the kids may be interested in.

Providence is a neat town. If a water-fire is scheduled, it's a one-of-a kind experience. Or, you can take the ferry to Newport for the day. Don't try to schedule too much into one or two days. This little state has a lot to offer if you can manage a trip back.
Nice thing about both towns is that they are walkable.
As a native Rhode Islander, I am never surprised to hear differing adjectives used to describe Providence. The city has gone through dramatic changes in a relatively short amount of time - most physical changes for the better, political, kind of gone downhill. But the people are passionate about the place and let it show.
I recommend getting info from your local AAA or the CVB regarding family oriented activities. Personally, when I take my family to Providence, it has been to have Indian food, to shop at Buck-A-Book, and to have a beer at Trinity Brewhouse (which, believe it or not, has a pretty family-friendly atmosphere.)

Enjoy your stay!