I think a lighter rug under the dining table would look nice.

Your table & chairs look a little more contemporary, so look for a large scale contemporary fixture, and a large print, colorful rug...maybe round...but large. Large scale artwork...not too traditional or a large mirror. Add metal curtain rod about 12" inches higher than the top of the window. Have it extend approx. 14"- 18" on both sides of the window, then add, long, double width, drapery panels that hang just covering the outside frame of the window.

The light you have now doesn't look Mediterranean so go with a less fussy look that will compliment the bleached wood table.

Dark hardwood floors are being added to the formal living and dining room to match these stairs. The lighting needs compliment the ceilings in the living room and dining room. New furniture will be added. These photos include the sellers furniture. I am open to ideas for both lights and furniture. There is travertine that will remain in the foyer and base of stairs. I would like to add wood to the dining room ceilings and replace the columns with wood beams.

It's a beautiful home. So many ways to go with it. You should first look for furniture you REALLY like, no matter the style. Once you either purchase some or just make a note book with photos, this is the place to start. It will help you to closer define the look you want. From there you can look for light fixtures, and even the types of pillars, trim, ceilings, etc., that would work best with it including flooring. If you find you really like dark wood furniture, maybe dark floors aren't the best options. I never like installing such permanent things like flooring without an overall plan. And the place to find the "look" you want is to choose furniture you like.

Excellent advice!!!

Thank you all for the comments and advice!!!

I can't see adding wood to those ceilings or replacing the columns with wood. I've just taken a stroll through the first page of your ideabook and I think you may have bought the wrong house. Beautiful as it is, it will never be this:

I was thinking that wood on the tray ceilings would go well with travertine floors

Hello Seraka, A lovely place you have!
I'll advise you to try to find out what you exactly like/want to achieve and also what NOT. Collect pictures from furnitures and accessories, wallpapers, fabrics etc. you like, also colors. At a certain moment you have many pictures; shift what you really like and paste that on a mood board. I made for you 2 examples. You can make mood boards per room. When you're shopping for furniture etc. you can take the moon board with you and stick to what you have chosen. Hopes this will help you.

@Diana. I really like the first board!! Thank you for the advice!!