This is a great question. The Old Testament contains a large number of books (39 of them). So, the geography is variegated, as you can imagine. However, if you want a general picture, there are three important areas around the Fertile Crescent.
- Mesopotamia. This area refers to the area between the Euphrates and Tigris rivers. The landscape is variegated - mountainous to the north, desert to the south, and lush by the rivers. Perhaps the earliest human civilization can be found here. Summerians, Akkadians, Amorites, Babylonians, etc. Many people see this area as the cradle of life.
- Egypt. What can be said of Mesopotamia can be said of Egypt. The Nile is particularly important, since life around the Nile is very fertile. We also see the great narrative of the Exodus take place in Egypt (as well as the life of Joesph). Finally, this is a great river culture, which produced powerful societies.
- Syria-Palestine. This area did not have a great river. In this region, there were smaller societies that were segmented. However, this area was connected the Fertile Crescent and therefore it was important for trade. In fact, it was situated at the door of three continents: Africa, Asia and Europe.
For more information, I suggest that you read an Old Testament introduction book. There will be many maps as well.