I'll start with Jamestown, one of the first colonies to make it. The beginning of Jamestown was almost it's end, the colonist were unprepared for the harsh winters there and were almost killed off entirely on the first winter. Thankfully the local Indians were around to aid the colonist until they could establish themselves. Eventually people realized that there was no gold or silver or any other valuable material around and people started to think maybe coming to America was a bed idea. Luckily tobacco arrived as a major cash crop just in time and thanks to the very fertile soil in and around Jamestown the tobacco industry boomed there. With the help of tobacco the Jamestown colony thrived. Without the soil to grow tobacco chances are Jamestown would had eventually just faded away, proving that the geography of Jamestown was extremely important to it's development as a stable colony.
If you want to look at it in a wider scope you can look at the early death and disease rate for the early colonies. Just imagine if the first colonies were found on giant plains, free of most of the more lethal diseases that plagued the swampy terrain of the early colonies. Since the death rate would have been lower indentured servitude would have been phased out sooner and slavery would have been adopted quicker. This could have had a major effect on the colonies future. What if it it's early adoption made it more commonplace then it already was, making slavery almost impossible to abolish in the South and even North. What if the rebellion slave owners feared so much actually happened, creating a new free black country in the process? How would another nation would have effected the development of the Americas?
Even bigger then that is if you consider the abundant natural resource the Americas provided to Europe. If the geography was different and most of America was just barren desert the colonies wouldn't even exist along with the current day US. Instead Europeans found a treasure trove of natural resources, spurring the interest of many and giving a valid reason for European colonization. From it's forest for lumber and game, bay's full of fish, and rich soil America provided the perfect place for colonies to prosper given a little work.
In summary I do believe geography was the primary force behind the development of the Americas. A colony may change ownership or worship a new doctrine but the colonists will always depend on the land around them to keep them alive and let them prosper. Without it they're nothing but monkey's in fancy clothes asserting their dominance over nothing.