At the time of the exodus, the Egyptian capital was in a town called Avaris, later called Ramses. Though there is some debate about where Avaris was exactly, the consensus seems to be that it was in an area now called Tel el Daba. [The link leads to a map, based on archeological discoveries, of the capital Moshe may have known.) Tel el Daba is at 30° 47’ N, 31° 50’ E.
Goshen, the district where the Hebrews lived, is generally associated with Faqus. If you scroll down just a bit from Tel el Daba, you will find Faqus, about 5 miles south of the ancient capital. Given that Moshe may have been put in the water a few miles north of modern Faqus, and that Bas Pharoh and her maids may have wandered a few miles south of the capital, the biblical account seems to match the geography.
Another neat point, courtesy of Google (and Robert Alter)
Center the map on Farqus, and zoom out so that you can see both Farqus, and some of the Sinai. Now click on the buttom marked "satellite." The delta region is green - lush even - while the dessert, of course, is bone dry. This stark contrast is used to great symbolic effect in the exodus narrative.
As Robert Alter shrewdly points out Moshe, from infancy, is associated with water. The water saves him, it's where the plagues began, and a barrier of water must be crossed by the fleeing Hebrews, water that collapses on the pursuing Egyptians and drowns them just as hebrew boys were drowned. Egypt, too, is associated with water, the Nile especially, and after their escape, the former slaves remember Egypt as a well-watered place of fish, melons, and cucumbers.
The wilderness, on the other hand, is noted for dryness. Moshe first meets God on a mountain called Horeb, which, per ibn Ezra, means "parched place" and at this first meeting, God reveals himself through fire. Later, at the culmination of the narriative, the mountain (now called Sinai; a pun Alter suggests on sneh) is surrounded by divine fire.
Though the Rabbis later associated the Torah with water, it seems that the Torah itself took the opposite view: In Exodus, water represents Egypt, and all that is corrupt, whereas God only makes himself known through fire, and in a place of heat and dryness.