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BOS is the airport, not the city. "Cheap eats in BOS" means sandwiches in a terminal. The city is "Boston."
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If you're in the near western suburbs, try Captain Marden's on Linden Street in Wellesley for seafood. The last time I was there three of us ate dinner, including soft drinks and a shared dessert, for $44 including tax and tip. You can spend more if you want lobster, but still in the "cheap eats" category - and pretty good.