To put it simply, peace tends to be boring. In most fantasy and sci-fi stories there is some war going on somewhere, and the characters somehow get involved to where they have to end the war to stop the bad guy.
Even so, peace can be useful. Maybe there's soon to be a revolution and the story starts in the "calm before the storm." Then the characters get caught up in the storm and have to find their way out. Whether that involves stopping the revolution or helping the revolution achieve its goals.
Peace is just the lead up to the conflict that drives the story forward and forces your characters to grow. And no, you don't need a drop down, drag out, country vs. country, citizens vs. government type of war. That's just an example. :P But conflict is necessary, because a story about a character who lives in peace all the days of his/her life is a non-story. There's no point to it.
Now, even though you're going to have a conflict begin, you need to know how your characters are going to act in peaceful situations. Peace effects a number of things that would be outside your character's control, and these things affect how your characters will act throughout your story.
Are their prejudices going to come out when they interact with a person of a different race, or are they going to treat them with tolerance? Do they like to make noise if things get to peaceful? Do they like to make conflict where there isn't any? If something (bad) happens right in front of them, do they just let it happen, or do they try and rectify the situation? Or do they join in on the fun? >:-) Are they champions of justice, and does that justice apply equally to all, or just to a few? Do they enjoy the increased trade, or bemoan it?
If you decide to have peace between your races, you need a conflict to drive your story. Whether you make that something limited to the character, or you extend it to your whole world is up to you. Just be sure you have your peaceful interactions defined before you jump into the war, since how a character acts during peace can be drastically different than when they're at war.