Two of my favorite bistros are within a couple blocks of the park: Fringale and Bizou.
At Bizou a few weeks ago, loved the shad roe pan fried with a cornmeal crust. the beef cheeks are a perennial favorite. Interesting wine list with nice selection of southern France country wines that go so well with the Mediterranean cuisine. We had the Haven Syrah from Carneros that was black as night and very rich - highly recommended.