If you drive ~45minutes north of Constanta, and follow the coast line, you will eventually come to Cetatea Histria. Its hard to go much further since the road ends.
This is an ancient site of the Roman capital of the region. It was a vital hub of agriculture, trade and patrol of the the Black Sea.
Its not huge, but definately not crowded. You can walk around and see everything in ~1.5hrs.
Of course if you come in summer in Constanta is not good for you to miss the beach but in winter if you come you'll have to avoid it becouse of the wind,but if the weather permit it you can go there is nice and lonely.
Mamaia is a popular beach resort about 3 miles north of Constanta. There are lots of shops and restaurants as well as a beautiful beach.
This monument was built, as commemorative plaque for the Romanian sailors, whose grave is the sea.
It is placed on the shore of the Black Sea, not far from the Casino.
The Ovidiu’s statue, placed in the Ovidiu Square since 1887, is for many people, the rendezvous place.
By night, the monument is spectacular illuminated and has a special grandeur.
the majority of the tourists are enchanted by the mamaia's beach or by the 'modern beach'. still there are also some nice beaches in the city's line that are worth mentioning ;)