I don't call a place an "institution" lightly. Only certain restaurants reach that status, and it means they're doing something better than all the other places. Consider Peter Luger and steak=institution. At Barney Greengrass on the Upper West Side, they do bagels and lox insanely well and have been for over 100 years. Alfred Hitchcock would order 10 pounds of fatty sturgeon at a time to be sent to L.A. - now there's an outpost in L.A. But nothing can compare to the feel of the Upper West Side location, and that you're in one of New York's great authentic Jewish delis. On the way upstate recently, we picked up two sandwiches at Barney Greengrass - smoked salmon, tomatoes, a bit of scallion cream cheese, and an everything bagel. No I couldn't finish the whole thing. But I could taste New York in every bite. Make sure you have cash - they only take credit cards on certain days.
They're also famous for their chopped herring salad, which tasted a lot like tuna salad to me.