"Remains" certainly may be used, but it's common to refer to these as "ruins".
High on top of a hill overlooking Athens stands the proud remnants of four of the most well-known ruins preserved from the ancient world. The iconic Parthenon, Propylaia, Erechtheion and the temple of Athena Nike make up the Acropolis of ancient Athens.
[The ancient city of Delphi] was also the location where the oracle of Delphi was filled with the spirit of Apollo and asked for guidance. Today, numerous ruins from the city remain
Under the Romans, [Corinth] continued to prosper, which explains why the most interesting ruins to view here are of Roman build.
Today Caesarea is a popular ancient archaeological site boasting extensive and well-preserved ruins. Its most impressive structure is the large and picturesque ancient theatre, which overlooks the deep blue ocean.
Perched atop an isolated rock plateau on the eastern edge of the Judaean Desert, overlooking the Dead Sea, the ancient fortress of Masada is one of the world’s most beautiful ruins.
The Haunting Beauty of Masada, Israel's Famed Ruins
and many more.
Formally, instead of "ruins", these may be referred to as "sites of archaeological interest", or something similar.