Gansett's are great lawn mowing beer, but really only a small step above Coors light. Right now the two best breweries in the state are Grey Sail (Captains Daughter is their DIPA - hazy New England style loaded with mosaic hops), and Proclamation. Grey Sail's Pour Judgement is also decent, but no where near the level of Captains Daughter. Everything I have had from Proclamation (IPA and DIPAwise) has been excellent--they are consistently putting out dank and juicy New England IPA's.
Right over the border in Stonington CT there is also Beer'd Brewing. Funky location with consistently good DIPA's, although in my opinion they are a little on the boozey tasting side (most of them are 8-9%).