I think Daddy Long Legs had one set. I bring it up because it's an example of how much you can do with props and lighting. The audience will suspend their disbelief.
The Great Comet is done with one set, but I could see regional theaters doing it with multiple.
If you are looking for plays or musicals that take place in one location. This season off the top of my head (besides what was listed already) I can think of Jitney, Master Harold and the Boys, Marie & Rosetta, Hedwig (not this season but still fits).
for me, I kind of think Mamma Mia, Hamilton and Kinky Boots are one set, as not much changes, I've only seen Mamma Mia and Kinky Boots 'live' and they are both successful to me, and so is Hamilton from what I've seen.
http://www.flickr.com/photos/27199361@N08/ Phantom at the Royal Empire Theatre