Of all the 2013 movies I saw (there are a good number I didn’t see), the best are American Hustle, The Spectacular Now, Gravity, Blue Jasmine, Populaire and probably Renoir.
Honorable mention goes to The Place Beyond the Pines, Enough Said, The Hobbit: The Desolation of Smaug, Kick-Ass 2, and World War Z.