Ovid, Tristia and Epistulae ex Ponto (AD 9–17). The most famous literature ever written about Constanța. Ovid was exiled to Tomis by Augustus and produced nine years of beautifully self-pitying elegies about the cold, the language, the barbarians and the absence of Rome. Any modern English translation (the Peter Green volume is excellent) gives a vivid if jaundiced sense of the city in the first century AD.
David Malouf, An Imaginary Life (1978). Australian novelist Malouf wrote a short, lyrical novel based on Ovid's exile at Tomis. The poet befriends a feral child and slowly loses his Roman self in the steppe. A different, deeper way into the same period.
Olivia Manning, The Balkan Trilogy (1960–65). Not set in Constanța specifically, but Manning's novels of inter-war Bucharest give an extraordinary picture of Romania in the months before the German invasion, and several scenes drift to the coast. A masterpiece.
Patrick Leigh Fermor, Between the Woods and the Water (1986). The second volume of Leigh Fermor's account of his 1933 walk from the Hook of Holland to Constantinople includes a slow passage through the Romanian plains, with one of the best descriptions in English of Dobruja's lost multi-ethnic culture.
Mihail Sadoveanu, The Hatchet (Baltagul) (1930). Not coastal — this short Moldavian novel is set in the Carpathian foothills — but it is the closest you get to the texture of inter-war Romanian rural life and is essential background reading.