Batcave in Arkham City

The plans are in the back of Quincy Sharp's office. GameInformer has a video walkthrough describing how to see the plans for yourself.

Side missions act as supplements to the main storyline, and will not affect your main objectives. While there is some overlap with the main story at some points (at least two of the side missions won't unlock until you get far enough into the main game), you will never be disadvantaged by doing one versus the other.

You will find that as you go through the game, there are doors/areas that you will not be able to access as they are a part of a sidequest, and will only be available to you when appropriate. You will never need to access these areas to finish the main story.