Paint a slightly darker color than the ceiling.

I would go with Benjamin Moore Cloud White. It is a beautiful warm white that has depth, would be stunning with your dark trim. Go with a flat\matte finish. By the way a very charming room.

We are adding a floating mantel...I will post fished pics...thanks for the help...

If the dining room has white trim what color white would you use for trim?

What I am noticing is that the dark timber and dark trim is weighing down your room. Is the entire house trimmed in this dark trim.?

You said the dining room is painted in white trim? If so, I would paint this room in white also, including the beams. This would instantly brighten the room.

What about the trim in the rest of your house? What color is that?

Everything else in the house is white trim....my partner doesn't want to paint them white....

Nice room, beautiful floor. If you want to make this room feel lighter, you should also think about a light coloured rug and furniture.
Brown or black leather furniture always looks heavy. If the rest of your home is lighter and brighter, you could consider embracing the relative darkness in this room and go for warmer colours.

Okay...I understand. So, this will be your sort of cozy room. I would

-change the can lights to led. They are super-bright. You will want a dimmer after you put them in. Expensive, but worth every penny.

-light colored rug and furniture, as Carolins mentioned.

-bright artwork and accessories

-mirrors
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As to your original question, I would pick up the gold tones in your floor, but keep it light.

Suggested color:

Bm rich cream 2153-60

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To answer your question regarding what colour to paint the trim in the Dining room, I would keep it the same BM Cloud White but in a semi-gloss. You still see the detail of your trim with the glossier paint against the matte walls. I agree with the other comments to keep furniture light and neutral, ie sofa, however you should inject colour/pattern in your accessories, ie decorative pillows, lamp shades, art work and even an occasional chair and/or ottoman. If you keep both the sofa and chairs neutral then you can add a touch of colour and pattern in an area rug.

RH Paint color Butter..lovely color,not a screaming yellow,and everything goes with it!!

Extend drapery panels on either side of the window approx. two feet to give the illusion that the window is much larger.

Sorry..did not realize you are looking for a white paint color..Cloud White is a great one.

Ok cloud white matte finish, and the trim in other rooms semi gloss....ceiling same color in matte finish ya think?

BM Ceiling paint matte CW.

I like the idea of painting the wood trim and beams white...this opens up lots more colors for your walls, soft ivory, or greens?