I saw Your Name (Kimi No Nawa) on the weekend. It's about a boy in Tokyo, Taki, and a girl in the countryside, Mitsuha, who start dreaming that they are the other person, even though they are complete strangers.
It was a popular movie in Japan, and is in a two-week run in some North American cinemas. There was a full theatre when I went to see it. Though I do live in Vancouver, which has a large East Asian population. Amusingly, I was the only non-white, non-East Asian person there.
The movie was quite good, with interesting and engaging characters. In particular, I thought it was "well-balanced". Some comedy, some drama, some romance, some moderate action, a touch of scifi/fantasy, a bit of Japanese religious mythology, and even an explosion.
One of the problems I have with modern western movies is that they seem to have lost that sense of balance, and often tend to extremes. An action move is 90% action with very little characterization. Romantic movies are intensely romantic. Indie movies tend to be very quirky and not very normal.
Your Name is also relatively short, clocking in at 1h 45m. Again, this is quite good, as it packs a lot in that short time frame.
Your Name is not a perfect movie, though the anime community hypes it up a lot. In particular, if plot holes bother you, there is one major plot hole, though it's not strictly a plot hole. On reflection, it's extremely unlikely the characters did not do or realize X. Kind of like characters not calling the police when they have a cellphone and in a situation which warrants it. But if you just let that go, or attribute it to the "magic dream" blinding them to it, it's more than good enough.
I recommend Your Name, especially if you can catch it in theatres. You may only have a week to do so, however.