There is no particular topic that you must write on, but it must be on American history before 1877. Prior to starting the paper I need to approve the topic you choose. This paper cannot be on the Civil War itself. Remember this is not a descriptive paper but an analytical one.
Most importantly, however, is that you choose a topic for which you can find good academically credible sources. Wikipedia.com, about.com, and your textbook are not the best sources (meaning you will get dinged for using them!). You will want to find an academic book (University of North Carolina Press for example) or a scholarly article (Journal of American History for example) on the APUS library page or other sources. Using just websites WILL result in a descriptive paper, and you want to write an analytical paper!
Guerilla tactics of the American Revolution
Social changes because of the Market Revolution
Indian Policy from Jefferson to Jackson
Significance of American military failure in War of 1812
Impact of Shayss Rebellion
Effect of Civil War on social issues
Reform movement of 1840s (prostitution, temperance, and others)