Downtown, if I want a great steak place, I go to Ruth's Chris.

For old school Italian, you should head to the North End, but that's a little bit of a hike from Downtown.

Good seafood in the seaport district:  Ocean Prime, also a bit of a hike from Downtown

So many great choices in Boston...

Here are just a few of my favorites...  (The North End is a short Uber or subway ride away.)

Island Creek Oyster
Yankee Lobster - excellent lobster rolls in Seaport district
Trattoria Monica - North End intimate dinning
Giacomo's - North End great value/food (a wait, but worth it)
Pizzeria Regina - get your pizza fix in with a classic
Top of the Hub - great view of the city (although if you're there, most won't notice it...)
 

Could only eat half as it was humungous...but supah delish and the service was excellent xo

if you want lunch...

Take a trek to Sam LaGrassa's downtown and stand in line with the boys of Boston business. The sandwiches are not to be missed. On the other hand you'll likely be busy Otherwise almost anywhere in Copley in good for dinner.

Select Oyster Bar is a favorite for drinks and seafood. The chef, formerly of Neptune Oyster, doesn't like lobster, which explains why his lobster dishes tend to be amazing (he needs to raise the dish without relying on lobster as a crutch). Try the lobster salad or the off-menu, lunch-only lobster sandwich (don't call it a roll).

Erbaluce in Bay Village/Theater District is some of the best Italian food in the city.

Sorellina (Italian) and Mistral (French) are some other great options.