Personally for me think they look beautiful either way. BUT, and it's a big but, I wouldn't want to have to worry about keeping a rug under a table clean. I may love to vacuum, but I it's just not so fun when dodging table can chairs under a dining table. It's so much easier to sweep a bare floor in this situation. But that's just me.

I would recommend either a solid color fabric, or a very soft, subtle pattern (almost tone on tone). The fabric on the chair seats and the chair backs already have quite a bit of detail, and the wood shutters bring in some texture as well, so I think your drapes should create a simple but elegant backdrop. My favorite look for drapes are ones that are fairly close to the wall color, (could be a tone or two lighter or darker) and that are hung from as close to the ceiling as possible, ending just above the floor (floor length, but not puddled). If you have enough room on both sides of your windows, extend the rod past the width of the windows by about 10-12", so that when the drapes are open, they can hang straight down with the inner edge just meeting the window, and not actually covering it. I personally love linen drapes, but if you want a little more bling, consider an edging like a Greek key in gold, or a silk drape that has some sheen). Double or triple the panels on each side, for a full look. Here are a few looks to consider. Going with a higher contrast drape, like a blue or green from your chair fabric or art, could look quite good too, but I'd still stick with a more solid color look. Please keep us updated with what you decide to do. :-)

Rug! Keep the Bohemian Modern chic vibe with a patterned Moroccan style like: https://www.rugsusa.com/rugsusa/rugs/rugs-usa-moroccan-diamond-tassel/off-white/200GCDI01A-406.html?utm_source=google&utm_medium=pla&adpos=1o5&scid=scplp200GCDI01A-406&sc_intid=200GCDI01A-406&gclid=EAIaIQobChMIi4Gx49ru2QIVyFmGCh12VwK-EAYYBSABEgJVHfD_BwE or this black rug would make a beautiful statement! https://www.westelm.com/products/samara-shag-rug-black-t3437/?cm_src=AutoRel or add some color and texture, blue will compliment your furniture nicely: https://www.westelm.com/products/ombre-batik-rug-t4257/

Is the wall portion on the right side of the opening deeper than the left( the one your hutch is currently on). Looking at your pic it looks like it could be...? If that is the case I’d move the hutch ( or sideboard) to the opposite wall. If you keep the hutch, I’d find Another place for the sideboard as both seem to be too much furniture in the room.