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You have terrific hardwood floors. They are a beautiful color and makes the room elegant. Also, your room has so much potential, with some simple modifications you will be able to have a dining room that will suit your family, dinner parties, and be the 'casual elegant' you are looking for.
First things first, the most significant changes you will be able to do that will dramatically upgrade your dining room would be to remove the wallpaper and mirror. Both of which you mentioned. These changes will instantly bring your room into the 20th century.
I like your idea of doing a burgundy color on the one wall with the photos and a cream color on the others. This will be a great starting point, the burgundy will be your accent color for the room - the idea of an accent color is to have one that contrasts with your color scheme and sprinkle it throughout using art and accessories. This moves the eye from point to point in the room - allowing the viewer to enjoy each of your rooms furnishings.
The first thing I noticed in your dining room was it seemed to be a little cluttered. Less is more. Your room will feel more cozy and complete with a fewer number of large décor items rather than lots of little pieces. I noticed you have a lot of picture frames throughout the room. I would recommended making a picture wall, you already have one started, the soon to be burgundy wall. Doing a picture wall is quite simple. Simply find an array of frames of different sizes, try to keep them all the same color and cluster them in a random but orderly matter on the wall. They will allow you to display all your favorite pictures and memories together, instead of having them spread out where they will be harder to view and appreciate.