I am the only programmer on this project and I would like to work on two different computers so I'm storing the project in dropbox. Should I check "Create local git repository"? What are the impacts?
Creating the local git repository means you will be able to version-control your source code, which I would consider a good thing. Now, having a git repository in a DropBox is dangerous in case the DropBox folder is shared, if two people change stuff at the same time in that shared git repository, you will end up in a DropBox conflict nightmare.
Assuming your DropBox folder is only visible to you, and you will not work on both computers at the same time (seems unlikely), it is absolutely fine to have the local git repository in the DropBox, though it will increase the space consumed off your DropBox account (that's pretty much the only side-effect, that and bandwidth usage for synchronization).