Tim, yes you will generally get better cash flow with a 3 or 4 family than a single or duplex. But as I mentioned, the tenants have a different mindset so it can be a bit more work to manage them. Good experience, though :)
Providence is big, so it really depends on the area. I know some investors who still won't go into Providence - a lot of folks were burned in the crash - but I think there are opportunities in every city/town. I wouldn't personally make a blanket statement, especially since there are so many different neighborhoods.
You'll get as good, or better, info being "on the ground" and driving through neighborhoods, and especially talking to neighbors, than you will by researching a city/town on the Internet and looking at "appreciation rates".
Talk to people, read the ProJo, check out the area yourself, to get a sense of what's happening and whether an area is improving or not. You can look at other indicators like sale prices, rents etc. but they shouldn't be the only part of the picture.
And of course, if you're going to live there you have to ask yourself if you want to live there. And similarly, how likely will potential tenants be to want to live there?