Montaup is okay, probably next on the list of publics. But it doesn't compare to the quality of the privates.
It is very short (6,400 yards, I think) and there are a few holes that run next to the highway. Some great views at various points. The last time I played there, it was a Saturday in summer and they were allowing fivesomes! It was one of the longest rounds of my life. I will only go back in the off-season.
Dan...Perhaps a little tough on Montaup. I have always found it to be sporty and enjoyable. First two holes, which are quite good, are along a side road with the highway on the other side of that road. Have not found it that distracting. Some very good green complexes with quick greens and lots of undulation, especially on the front. Always in excellent shape especially for the amount of play.
Typically don't play there on the weekends but pace of play has always been an asset not a liability. Can usually get around in 4 hours or so. It is a bit short but offers different options of angles off the tee for best angle of attack to the greens, especially on the front. The front and back are a bit different. No architect is listed but the front has always seemed 'older' and a bit more classic in design. Have always thought that perhaps 9 were added and the back has a Cornish feel to it. Overall worth playing.
One course in RI that is never mentioned is Crystal Lake in the north eastern part of a very small state. Semi-private course that is never crowded. About 5 years old. Farm land, links style with fun greens and overall an excellent public for a state with few good public layouts. Would probably rank it 4th - Newport National, Triggs, Montaup, Crystal Lake - then not much.