My wife and I saw this much talked about movie yesterday.
I think it's very good for 3 main reasons:
1. Emma Stone is utterly charming and fantastic and they should just send her to Oscar now and tell the other contenders there is really is no point in them coming to the ceremony.
2. It's very pleasingly directed, and avoids, in large part, the annoying over-editing of dance sequences that has afflicted modern musicals for so long. I only read up on director Damian Chazelle after seeing the movie - 32 years old and obviously very talented. (He co-wrote 10 Cloverfield Lane too - quite a genre difference there!)
3. The dancing is just right for this type of movie, in that it doesn't overwhelm with technical virtuosity in the way that Fred Astaire or Gene Kelly always seemed to be dancers trying to act (this movie is the reverse), and it shows how well non professional dancers can do if they practice enough. I think it makes the viewer feel capable of sharing in dance, too, even if it's never attempted.
It's not a perfect film - personally, I think the final interaction between Stone and Gosling should have been more intense, and some of the music tends to the bland. Would I have been happier with a less melancholy story? Perhaps, but it is what it is, to quote from the recent episodes of Sherlock.
It's well worth seeing.