Yeah, there's the mall (with Dave and Busters). Fire and Ice is also a great place to grab a bite to eat. There's also a zoo not too far from where the mall is that my wife continually talks about (she's from RI). If you're driving to RI, you could spend a day in Newport (about 30 minutes south of Providence); it's a pretty big tourist town. There are about 7 different mansions that you can tour there (The Breakers is freaking insane and is the grandest in Newport).
I'm sure I could get more suggestions if I asked my wife.