The analogy essay requires a student to explain one thing in relation to its similarity to another. Often the two things are not closely related on the surface and through analysis the similarities become clear to the reader.
Choosing a good topic in this style requires a little of each of the following:
Everything is made up of the same basic stuff. On a molecular level we are all fairly similar so finding a way to connect any two things just requires the patience to look past the obvious and see the rest.
A topic may seem good but later show itself to not be usable because it requires the write to engage in far too much research for the given time frame.
Some topics have been written on so much that if anyone new writes them, they will undoubtedly add nothing original to the conversation. Even a very good writer would find him or herself producing work that gets easily overlooked because someone else has written on the subject with more clarity and done so years earlier.
You can easily say one thing is like another or brings another to mind but the moment you say that it actually is something else, you cross the line into metaphor. As you think of potential concepts, make sure to phrase them properly or you will end up writing a different sort of essay altogether and that is not your intent.
With the preceding tips in mind you can begin brainstorming. Some of the ideas you might come up with are as follows:
The topics you just read are concise and can appeal to many different types of readers and writers. If any one of them stands out to you, try writing on it just for practice to improve your skills for later.