What foods to cook in a new cast iron skillet that will help improve the seasoning? I've never cooked with cast iron before and just picked up a couple Lodge cast iron skillets  (6" and 12"). They come preseasoned, but I imagine some additional seasoning is desired. 

I tried bacon, which took a lot longer than I expected, and left a lot of brown bits. I also tried grilled cheese, which wound up being a terrible mess that I threw away, since so much of the bread stuck. I had buttered the bread, and put some oil in the pan, but still went back to my non stick pan.

I know there are some foods that really require a good season on the skillet to cook properly (like eggs). Are there any foods that help improve the seasoning?
To improve seasoning, any frying or searing will help. Frying chicken, searing steak, etc. Anything that has to do with heating oil. The things that can damage the seasoning are acidic mixes, and in long duration. An example: Simmering tomato sauce.

I would also like to add that actually seasoning the pan, and proper handling and storage will give you much better results in improving your seasoning. One good starting point is Kenji Lopez alt's advice on cast iron pans. There are other very good sources on this too.