Schaff, Philip. "Ch. 28: Place of Composition." The Oldest Church Manual Called the Teaching of the Twelve Apostles. Second Edition, Revised and Enlarged. New York: Funk & Wagnalls, 1886, 123-125
Schaff considers the Didache to have been written most likely in Egypt, Syria, or Palestine (Schaff 1886, 123). However, the reference in the eucharistic prayer of 9:4 to bread scattered over mountains would be unlikely in the Nile valley. Further, in that region, there would be little thought about warm water for baptism (7:2) (Schaff 1886, 124). Syria makes more sense, as long as the composition is early, before Ignatius.
The use of Matthew's Gospel may suggest composition in Palestine (Schaff 1886, 124). The church at Jerusalem would have travel of apostles. It was never strongly Pauline. However, Antioch would also be a strong candidate. Schaff remains uncertain as to the place of composition.