Well in general, shore diving is the best way to find the tropicals so you are in luck.
You'll tend to find the tropicals in 20-30 ft or less. As you'd expect end to avoid the deeper and colder waters. They'll usually be found hanging around, or even under rocks. So shallow rocky shore dives are the way to go. The water temperatures were running in the mid-sixties in the shallower waters around Wetherill last weekend.
For tropical hunting the most popular site is Ft Wetherill in Jamestown. Vis at Wetherill is pretty hit or miss (can be 0, can be 15 ft on a good day). It is usually pretty crowded, though post Labor Day it may be less so. It is also pretty sheltered from everything but winds or swells from the south to southeast so it is usually diveable. Just stay shallow and hug the rocks on the edges of the cove or around the point between the coves.
There are also some very good and less known alternatives. King's Beach in Newport RI is a nice easy dive, plenty of good rock formations to look for tropicals around, and mostly better vis than Ft. Wetherill unless the seas have been rough. The catch is that Kings Beach is more exposed, so Wetherill will be divable on days that Kings Beach isn't. Like Wetherill it will usually be busy, though not quite as extreme.
There are several sites in Narragansett, but probably the best bet for tropicals is Pier 5 (aka Monahan's Dock) at the end of the sea wall south of Narragansett south of Narragansett Town Beach and the Coast Guard House Restaurant. Simple entry and exit by the boat ramp. However, it is very shallow (tough to get below 20ft unless you swim a long way out) and it is very exposed so surge can be an issue.
There are a number of other sites too, some of which are probably nicer dives, but for tropicals those three are probably best bets, and the other sites have much tougher entries and I am not sure how much hiking and rock climbing you are willing to do. Although being from Maine you're probably used to that, so I'd be happy to fill you in more on those if you are interested.
As for fills, there are three shops in southern RI near these sites, Ocean State Scuba in Jamestown, Newport Dive Center (down side is getting into downtown Newport with all the traffic on a weekend can be a real pain), or Narragansett Pier Dive Shop in Narragansett near Pier 5.
And for tropicals you might see.... most common is probably the spotfin butterfly and short bigeye. Some less common ones are the snowy grouper, lionfish, cocoa damsel, cardinal fish and trigger fish.
