Tutto Il Giorno Southampton presents Italian cooking in a garden-centered setting on Nugent Street. Brought to Southampton as an offshoot of the original Sag Harbor address, it is distinguished by a sprawling garden courtyard that encourages al fresco meals and welcomes canine companions. The menu leans on regional Italian ingredients; simple plates such as North Fork grape tomato with eggplant and mozzarella exemplify its direct, expressive flavors.