I like the color of your lampshade against the furniture. That might be a way to go adding color and pattern with things like a rug, art and accessories.

I painted Wilmington Tan by Bennjamin Moore with my Cherry Cabinets and wood floors. Looked great.

If this is a dining room, go neutral on walls in a deeper tan, beige tone. Then when you decorate for holidays nothing will clash between table and walls. Consider an area rug under the table/ seating area to limit the floor exposure to only near the walls. I too had same color flooring with my darker wood furniture and a floor rug helps a ton!

I like your blue with the cherry, and I agree with my friend Darzy that once you put the room back together with furniture, artwork and accessories, things will start looking as you wanted them to look.

I agree with Darzy that the peachy beige next to the dining room that is fighting for attention. It's competing with the blue and the cherry furniture. Don't know yet what color would work there--maybe something lighter. Also, the dining room could use a chair rail and/or crown molding. All the suggestions above are a very good start.
Just wanted to add one more thing: you'd be amazed at how much framing that opening between the dining room and the adjoining room would make. I'm thinking framing it with woodwork, you can look it up for ideas, and I'm thinking a medium-dark wood--it doesn't necessarily have to be match your cherry furniture--or even more of a blond wood to go with your floor. It would really dress up the dining room. Good luck!

I happen to agree with you. Blue is a lovely color, but I'd rather see it somewhere else. And I agree with Darzy. The color in the next room is not a great compliment to the floors. Perhaps you could paint the area between the two rooms an off white to minimize the color difference.

Buy a few samples pots of paint. Use them to paint foam board then prop them a few feet apart around the room. Look at them for a few days at different times of day eliminating them as you go. You will narrow it down and find the right color before doing all that work again.

I like these colors:
1) Classic: http://www.benjaminmoore.com/en-us/paint-color/grasslands
2) Elegant: http://www.benjaminmoore.com/en-us/paint-color/barefootinthegrass
3) Timeless: http://www.benjaminmoore.com/en-us/paint-color/mountainlane

Nice floors and the blue is pretty! Maybe if you carry it into the next room it would blend better? :) Otherwise here are a few suggestions for you! Best wishes! :)