I saw there wasn't a thread on this yet, and the Seaport area continues to change every day, so it's worth calling out some of the new options (and mourn a few of the old ones) for this year's PAX East. I work on Summer Street near Downtown Crossing, so I've tried most of these places myself and can vouch for their tastiness. Over the past few years the whole Seaport area has just exploded, and the number of quality restaurants and bars around there is incredible. Where it used to be a food desert, it's now a trendy and busy area of town with lots of options. As always, go by the Google reviews in the area, but if you want any suggestions, I've tried all of the below and can vouch for them.
Legal Harborside - Still the best Legal in the area. Down the street from the Renaissance.
Harpoon Brewery - Their food options are still limited to their great pretzels, but the beer selection is nice and the pretzels are tasty, plus the space is a ton of fun.
Flour - This is it chief. I love Flour almost as much as I love coffee and pastries. Sits down a side street off Congress St.
Blue Dragon - A fantastic fancier restaurant tucked off Summer St. American-style asian food, with lots of Chinese classics mixed in. Try the chicken feet!
Bon Me - A classic eatery with pork pate sandwiches and pickled veggies. Just a short walk from the BCEC.
Smoke Shop BBQ - This is a great BBQ joint with a huge number of soul food standbys and a big whiskey menu. Very good BBQ and worth a trip, about 0.5mi from the BCEC.
Committee - If you want a nicer mediterranean dinner, this is the place.
Shake Shack - They opened one of these on Seaport Blvd, about 0.3mi from the BCEC. Good for some quick eats.
Tatte - About 0.5mi from the BCEC near South Station, it recently opened up and has a great selection of upscale cafe fare like egg tartines, fancy pastries, and entrees.
Amateras Ramen - Down in the leather district near South Station, this is a common lunch spot for me and serves pretty authentic ramen.
Sweetgreen - They opened one of these near Seaport Blvd, about 0.2mi from the BCEC. Upscale salads that are really nice, but expect a line at lunch.
There are so many other options in the area - Lolita, Row 34, Les Zygomates - but these should help you get around the immediate area around South Station and the BCEC.