SRV is currently my favorite restaurant in the Boston area. Chickadee is also great and so is Oak + Rowan. (Links are to my reviews as @digga already linked you to their websites.) How they stack up against similar restaurants in NYC and LA I do not know, not having eaten in either of those fine cities in a long time.
For seafood, Island Creek Oyster Bar and Row 34 are generally well-regarded, as is Neptune Oyster with the caveat that they do not take reservations and the lines can be very long (although friends waltzed right in at 2 pm on a recent visit). I cannot personally vouch for any of these three seafood spots.
Oleana in Cambridge is a perennial Board favorite and well-deserved. Harvard Square has lots of food but not a lot of great food other than the omakase at Café Sushi for which reservations are required but not always easy to score.
If you want to eat in the North End, Mamma Maria at the high end and L’Osteria at the homey end, plus Modern Pastry or Mike’s Pastry for cannoli.
ETA: I see you know all about Neptune and tomatotomato beat me to Oleana.
