Another vote for Lee's Tavern here. It's right by the Dongan Hills train station so if you choose not to drive to SI and take the ferry instead you can hop on the SIR (don't be afraid, it's the same 2 bucks as the subway and a free transfer if you took the subway to the ferry in Manhattan) and ride about 12 minutes. There's no sign, it just looks like a corner bar. You can eat in or take it to go, they don't deliver because they don't have to. Locals are willing to order and pick up. It's that good.
Caveat: if thin crust is not your thing, then you'll hate it.
When was the last time you ate at Basilio's? They repainted the main dining room and reworked the menu under a new chef within the past year. Is it Babbo-level Italian food? No, but it's pretty darn good for what it is. One of the best Italian-American red-sauce places around.
Of course, if well executed Italian-American comfort food isn't your thing, then don't bother.