Eater Boston states (via a Facebook post from the place) that My Diner on A Street will shut down at the end of business hours on Sunday after being in business for 12 years, with the dining spot giving a glimmer of hope to customers, telling them to "Stay tuned for news on our possible reopening in Spring of 2017." At this point in time, it is not known where exactly they might open back up; there had been talk earlier this spring that they could return to the site once the residential development is built, as the structure will have space on the first floor for a restaurant.
Williams Tavern, a bar that is located next door to My Diner, is also disappearing, as it is housed in the same building that is slated to be torn down this summer.
The address for My Diner is 98 A Street, Boston, MA, 02127.
[Based on information from a @FortPointer post, it appears that My Diner probably wouldn't be moving into the new development because the proposed retail space would be less than half the size of the current My Diner space (only 536 square feet).]
[Earlier Article]
Williams Tavern and My Diner in South Boston Face Uncertain Future Due to Development
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[A related post from our sister site (Boston's Hidden Restaurants): List of Restaurant Closings and Openings in the Boston Area]