According to a Facebook post on the Quincy Is Everything group page, The Ice Box on Quincy Shore Drive at Wollaston Beach is going to become The Baja Box, with the ownership remaining the same and the place offering street tacos in addition to ice cream. An article from The Quincy Sun mentions that the spot will open in April and it will serve "tacos and related food in addition to ice cream and beverages."
The people behind The Ice Box/The Baja Box also run The Clam Box next door.
The address for The Baja Box is 793 Quincy Shore Drive, Quincy, MA, 02170.
[May 22 update: Eater Boston states that The Baja Box is now open, and it is serving tacos, tortilla soup, Mexican street corn, nachos, and chips and salsa, along with ice cream and Richie's slush.]
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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]