The weather in Boston doesn't allow for much dining "al fresco" so there aren't that many restaurants with big outdoor areas. There are some places in Faneuil Hall, on Boylston and Newbury Street. A very popular spot on Newbury is Stephanie's - the food and drinks are really delicious, but you will pay for that prime real estate on Newbury. Parish Cafe, VOX, Abe & Louie's, Atlantic Fish Company and Vinny T's are all lined up right on Boylston near the Prudential Center with their outdoor tables. The Rattlesnake on Boylston has an upstairs roofdeck that's a good option for outdoor dining in Boston when you don't want to deal with all the foot traffic going by.

If you are around the North End/Financial District/Aquarium, there are also some options in that direction. Joe's American Bar and Grill, while not the most unique Boston eatery, does have a nice outdoor area right on the water. Next door to that is a good local place called the Sail Loft that has cheap beer and good eats - they even have some good seafood on their menu. Tia's is also right there across the Christopher Columbus park and they have good lobster deals in the summer. Tia's isn't a place known for its food though, it's more of a "meat market" for the after work crowd.  Speaking of lobster and seafood, The Barking Crab is a fun summer spot for outdoor dining. The prices are a little high for what it is, but it is a must do if you visit Boston in the summer (and you should definitely like seafood in the first place!).

And if you don't get lucky finding a place with actual outdoor dining in Boston, most every place in the "touristy" areas opens up their tall windows so you feel like you are outside.  Virtually every restaurant on Hanover St in the North End will open up their windows and let all the delicious aromas waft out and there is some great people watching in that area - also very few homeless people or panhandlers so you will be safe to sit right next to the sidewalk. One last place worth mentioning for it's great food and outdoor dining is Ristorante Fiore in the North End. They have excellent Italian food and their rooftop deck is so relaxing and romantic.

Here is another list to check out: