Coming to Boston and looking for...
We are staying in the financial district and looking for some great eats.
Looking for...the best ramen, Szechuan, and other not-to-miss ethnic such as Thai, Greek or Indian.
For Italian is Giacomo's still good?
Since you are not getting any responses, I will chime in. Haven't been but Yume Wo Katare in Porter Square seems to get all of the press for Ramen (with long lines). Nothing spectacular downtown that I know of. IMHO Gourmet Dumpling House is the best place for Szechuan (and Taiwanese) downtown, although New Shanghai, despite the name, has a very good Szechuan menu. Giacomo's is still good for Italian if you don't mind the wait. The top two places, which are expensive, in the N. End are IMHO are Mama Maria and Prezza. Not great Thai, Greek or Indian downtown, although good Vietnamese (Xing Xing) and Malaysian (Penang). Hope that this is helpful.
Montien is probably the closest decent Thai and Penang is good Malaysian, both close. If you don't mind expensive, Prezza is my choice for Italian and if you consider French "ethnic", your right near Les Zygomates which is very very good. Also not far from Erbaluce which is an experience if you love Northern Italian and subtle.
Something else to consider for visitors is that we (Eastern Seaboard) have access to some European wines that other parts of the country don't get (in particular Portuguese and Spanish for Boston, but also French and Italian). While Toro has some decent affordable selections, the combination of Estragon and TdH have much broader selection and more reserve wines. Probably not what the OP was looking for, but a consideration for some.
Depending on whether you're up for an excursion, Gran Gusto in Cambridge has wonderful Italian food.
I've also heard that Yume Wo Katare is supposed to be fantastic for Ramen. I haven't been myself, however. Be prepared to wait in a long line.
Currently, my favorite "ethnic" restaurant in Boston is Myung Dong 1st Ave. in Allston. It's a Korean Soju bar/restaurant. They happen to have a killer bowl of spicy ramen soup as well, if you like that. The other not to miss items are the basket of mini dumplings, Cheese Labokghi which is a large bowl of ramen noodles with the Korean style Ddok Bokghi rice cakes, in a spicy tomato sauce with some cheese on top. Kimchi pancake, and the Gyeran Malee (a korean style omelet with ham and cheese or Kimchi). Also, if you have a few people in your party, make sure to get one of the Soju specials like the "Charles River", which is served in a goldfish bowl with gummy worms and large straws. They play Korean pop videos on the TV's and it's almost like being in Seoul. Lots of fun.
Best way to get there is a taxi or the Green Line "B" Boston College branch to Harvard Ave. stop.
Sichuan Gourmet is my favorite sichuanese place and is accessible via the green line though the New Shanghai in Chinatown also does a good job. i brought someone from Chung King to S.G., and she was pretty happy about the food.
Not exactly Greek, but Oleana has excellent middle eastern food; it is located in Cambrige. It is not cheap.
There are a number of good Thai places; I am not sure which one to recommend Rod Dee in Porter Square or S & I.
For Italian, i like Coppa and Rialto.
In addition to the ramen suggestions below, Uni serves late night ramen after 11pm on Thursdays, Fridays, and Saturdays. I think it's $11 for the bowl.
You're quite close to Chinatown, which has a lot of threads you can search on. In the North End, I'm a big Prezza as well as Taranta fan. Some people like Regina's. If you're a pizza person, it's a good bet, though I still prefer Santarpio's in East Boston. Speaking of East Boston, take the blue line to Maverick and search out the delicious Hispanic options in the area.
Another idea is Shojo in Chinatown. It's definitely on the swanky side for that neighborhood. Really modern takes on food from all over Asia.
Professional food writer in Boston here. In my opinion, the best chinese/szechuan/thai/asian food in Boston is:
1) The Gourmet Dumpling House.
There is no better Asian fare in the Hub. There just isn't, trust me I have tried to find better. Everything is good.
2) Uni Midnight Ramen
Only served after 11:00 p.m. on Thurs, Fri and Sat. The closest ramen that is better is Ippudo in NYC. Amazing pork buns.
3) Myers and Chang
Like the GDH, everything on the menu is solid. I reccomend Etsi's Hot and Sour Soup and the salmon.
For Italian food:
Ironically, the North End has pretty bad Italian food IMO. I think the three best Italian restaurants in Boston are
1) No. 9 Park
3) Coppa (the pasta)