I've done some quilt restoration, so I may have some tips to help. Do you have any idea how old the quilt is? I can't tell by looking at it. Perhaps you can't either. If you have any intention of cleaning it, do not dry clean it. The older fabrics were never meant to be dry cleaned, and the dry cleaning process can do irreparable damage to your quilt. The first thing I would wash it in is Retayne. It's a product out now that will "set" the dyes in the fabrics and keep the bright and clear, and most of all, keep the from running. You only have to use it once. I didn't use it on an old quilt top, and the colors ran badly in cold water while using a soap recommended to me by a textile restoration specialist. It ruined this irreplaceable quilt top. I was heart broken. Then if you ever have to wash it again, make sure to use a non-phosphate soap, something like a quilt soap, or a baby soap (like Dreft), or even baby shampoo. Do not use fabric softener. It just attracts dust to the surface, and makes it dirty faster. A bit of white vinegar in the rinse will not only release all last vestiges of soap (soap also attracts dust and dirt), but it will act as a minor fabric softener.
But you weren't going to wash it, so let's move on to repairs. First of all, gently press the quilt. That will move things into place so you will be able to see where there is actual loss of fabric and/or batting. Address the batting first. Freshen up the edges of the ragged batting that is left. Using scraps of batting, fill in the empty spaces, and either use the fusible tape to bond it to the nearby batting, or if the area is too small, or if you'd rather, just stitch the batting into place. It's critical that you do nothing more than fill in empty space, and not change the shape of the quilt. In the one area where there is a "hunk" missing, you can do one of two things. Pick complementary colors, cut them to fit -- looks like you'll need two there, and I don't know what on the back. Make the seam so it fits down the center of the original seam. Then carefully hand sew it in place. A slightly less noticeable approach would be to remove the entire two sections of the patch, make completely new patches for the area, and sew them in. The motif then remains exactly the same, and if the colors are reasonably close, no one will pay any attention to a slight difference in color. Then you just have to fix the quilting.
Where the fabrics have separated, put a fusible web underneath (after the area was pressed once, and then press it again, stretching the fabric as far as it can reasonably go. Don't over stretch. If you can't get the fabrics to meet, you could try a color coordinated satin stitching, and see if that reaches across. That failing, a color coordinated and appropriate small appliqué should do the trick.
Just one more word about washing. Our ancestors never washed their quilts the way we do. They would go years without washing them. Washing clothes was hard, so they washed only what was dirty and smelly. So they washed sheets, but not the quilts that went over the sheets. What they did do on a regular basis is either take those quilts out and beat the dust out of them (which I don't recommend for an heirloom) and then left them out in the fresh air to "air out". This was done at least twice a year, and made for sweet, dust free quilts. They also spot cleaned their quilts as necessary. Fels Naptha was my Grandmother's and Great Grandmother's favorite for this, and I use it too, for lots of things. It's a heck of a lot more effective than Spray and Wash, and considerably cheaper too! In her later years, my Grandmother, and then my mother, took to vacuuming their quilts to get the dust out. I don't mean applying direct suction to the quilt. They would take a piece of nylon stocking, put it over the widened end of the vacuum, and simply keep vacuuming the quilt. That way, dust was picked up, but the suction never "sucked in" the material of the quilt. The nylon made it much, much gentler. Then they would put a clean sheet out on the dry grass, out of direct sunlight, and lay the quilt outside. Sometimes they'd leave it out for a couple of days, and just keep turning it over from time to time.
(Sunlight is hard on quilts, so keep it out of the direct sun if you can). When they came back in, they smelled so sweet!
So I guess I'm saying that you can clean a quilt without soap and water, and do minimal trauma to the quilt. (The average washing takes 5 years off a quilt's life.)
You say you want to hang it. Remember, you are hanging old fabric. If there is any way you can attach fresh fabric to the back of the quilt, so the quilt is hanging on new fabric, that would be great. The old fabric needs structure and support. Put a new back on the upper third of the quilt, and run a rod across the entire top of the quilt. Attach the quilt hanger to that new rod, and that that rod and the new fabric carry the weight of the quilt. It'll make a huge difference for the quilt, and is not that much more fussing around.
I'm tell you these things because, mostly, I learned them the hard way, and I'm hoping you learn from my mistakes. You have a beauty of a quilt there. Do it justice!
Best of luck!