I would like to say "I am eating in the grocery store", and so far I have come up with "edo in foro" and "edo in emporio". But I'm not sure if either of these would be the best fit. What word would you use to describe a modern-day grocery store? On a related topic, what is the Latin equivalent of the Greek αγορά? I assume that if I were to ask the same question of Attic Greek, αγορά would be the clear choice. Please correct me if I am wrong.
The word to use is probably macellum. Lewis & Short offers:
macellum, i (macellus, i, m., Mart. 10, 96, 9), n. root μαχ-; cf. Gr. μάχομαι, to fight; cf. μάχαιρα, μάχη, and mactāre; prop. butcher's stall, shambles; hence, transf., meat-market, provision-market (where flesh, fish, and vegetables were sold). Lit.: venio ad macellum, rogito pisces, Plaut. Aul. 2, 8, 3: apud emporium atque in macello, id. Am. 4, 1, 4: nostin' porticum apud macellum hac deorsum? Ter. Ad. 4, 2, 34: excandefacere annonam macelli, Varr. R. R. 3, 2, 16; cf.: putarem annonam in macello cariorem fore, Cic. Div. 2, 27, 59: barathrum macelli, Hor. Ep. 1, 15, 31: quae est ista laus, quae possit e macello peti? Cic. Fin. 2, 15, 50: dispositis circa macellum custodibus, Suet. Caes. 43: cetariorum, Varr. R. R. 3, 17, 7: ad ipsum introitum exspectare macelli, Juv. 11, 10: retibus adsiduis penitus scrutante macello proxima, id. 5, 95.
—In masc.: conturbator macellus, Mart. 10, 96, 9.
—Plur.: fercula nullis ornata macellis, Juv. 11, 64.
—* Transf., meat: arcessitur inde macellum, Manil. 5, 370.
Meanwhile, to go grocery shopping would probably be obsono:
obsōnō āvī, ātus, āre, o)ywne/w, to buy provisions, cater, purvey: cum fide, T.: Vix drachumis est obsonatum decem, T.
—To feast, treat, furnish an entertainment: de meo, T.
—To provide, prepare: ambulando famem, get an appetite.