I would probably checkout Equinox Flower
Another goodie I've seen recently, and would like to suggest: Barton fink (1991)
Awesome in it's own way
I've seen Barton Fink. I love the Coen Brothers. I loved Fargo, No Country for Old Men and True Grit. I can't wait to see Inside Llewyn Davis. The trailer looks really good.
Regarding 2046, it's important to understand its context for maximal enjoyment. First of all, it's a Wong Kar-Wai movie. That alone means a lot. As others have said, and I concur, the more you put into a Wong Kar-Wai film, the more you get out of it. Aside from his stunning cinematography and beautiful soundtracks, you need to pay attention to his non linear narrative, and often confusing mode of storytelling. Watching his films two or three times in a row helps. But there's more as well. 2046 is the third in a loose trilogy, beginning with Days of Being Wild and In the Mood for Love, both highly acclaimed films. Watch them in any order, but watch them all, to pick up deeper nuances to the story in each of the three films.
Regarding Equinox Flower, you don't just watch Equinox Flower. What you do is embrace Yasujiro Ozu, get familiar with what others are saying about him, and then make a whole hearted attempt at watching all of his films from 1949 onward. You'll be happy you did. And likely decide they are your desert island films as well. It's very possible that this is the most important paragraph you've read all week, and if you follow the advice in this paragraph, your appreciation of cinema will double, if not triple.
But once you've done that, you've implicitly made the decision to watch mid 20th Century Japanese melodrama. Ozu's friend and contemporary Mikio Naruse made some highly acclaimed films as well. And thus, you should, and will, proceed to watch all of Mikio Naruse's work. Start with When a Woman Ascends the Stairs.
And from there, you will have become intimately familiar with the two actresses Setsuko Hara and Hideko Takamine, two of Japan's favorite actresses from the 20th Century. And thus you'll start seeking out the films of Keisuke Kinoshita.
But at that point, you'll be so smitten with these films, that you'll also be seeking out films by Kenji Mizoguchi, Masahiro Shinoda, Shohei Imamura, Nagasi Oshima, Masaki Kobayashi, Akira Kurosawa, and Hiroshi Teshigahara, as well as others.
These are the must watch Ozu movies:
Late Spring
Early Summer
Tokyo Story
Early Spring
Tokyo Twilight
Equinox Flower
Late Autumn
The End of Summer
Floating Weeds
An Autumn Afternoon
And chances are very good that those will become your desert island films.