Well, assuming you'll be at the Sheraton in the Back Bay (Dalton St.), you're just across the street from one of the premier dive bars in Boston which, IMHO, is a must when visiting our fair city: Bukowski's. How can you not love a place that offers "White Trash Cheese Dip" on its menu?
Also, Jasper White's Summer Shack is across Dalton Street from the hotel entrance. It specializes in local seafood. Very casual and pretty good food, though I personally think it's over-priced. But, people seem to like it. There are a ton of places along Boyleston Street in that stretch, but they tend to cater to the college crowd, and are a little more than "casual".
If you want to go a little nicer, across the Square of the Christian Science Mother Church, in the 1st floor of the Colonnade Hotel is Brasserie Joe. Very popular, good food, and not too terribly expensive (for Boston).
That's all the comes immediately to mind in close walking distance to the hotel. I'll put on my thinking cap and come up with a few more.

Also, Jasper White's Summer Shack is across Dalton Street from the hotel entrance. It specializes in local seafood. Very casual and pretty good food, though I personally think it's over-priced. But, people seem to like it. There are a ton of places along Boyleston Street in that stretch, but they tend to cater to the college crowd, and are a little more than "casual".
If you want to go a little nicer, across the Square of the Christian Science Mother Church, in the 1st floor of the Colonnade Hotel is Brasserie Joe. Very popular, good food, and not too terribly expensive (for Boston).
That's all the comes immediately to mind in close walking distance to the hotel. I'll put on my thinking cap and come up with a few more.