I found this picture in a magazine this month and thought it was so much fun. It is a formal room but adding this fabulous oil painting of a heart adds some whimsy and incredible character. This goes to show you that even though it's formal, it doesn't need to be "stuffy". There are a lot of patterns and textures in this room but they all work together. Pretty monochromatic furniture with big bold pops of color which is what makes this rooms many patterns work well together. I thought this ottoman was very creative and gives a relaxed feel to this sitting room. Of course the chandelier adds a softness to the bold painting. Notice that this room has paneling in it too. Paneling is pretty outdated. However in this room, because of this large scale painting on the wall, it distracts from the paneling and puts the focus on the painting instead.
Don't get stuck with labeling your rooms. If it's your formal living area, it doesn't NEED to have all formal items in it. Adding fun elements to any formal room makes in feel more inviting. Formal living areas are often just wasted space and just "for show". I challenge you to make your formal room feel more casual by adding some unexpected "casual" items to it. Once you do that, you will find that your room is used more because it feels more relaxed, making your guests less intimidated with the space. Every square inch of your home should be USED, not just for show.