We faced the same problem a few years ago. Because the ceiling was low, we opted to install can lights in the empty space. There are 8 lights in the space and 3 in the soffit.

Maddielee makes a good point - how high is the lower part of the ceiling (i.e. if you just sheetrock it to make it level with the rest, how high will that be)?

Embrace the space -- and allow that newly re-finished space to show off that wonderful light! And that higher space really does make the room look taller! :)

Before I'll answer I'd like to know what's under that space?

Maddielee that's a great option looks great in your kitchen, I wouldn't have been able to see it without your pic. It also takes care of not blading with dining room pendant.

Sjhockeyfan I am sure I should know this, but it seems almost every room in the house has a different ceiling, I will check the height tonight.

Embrace the recess...you can put in cove lighting if you want, or I have seen them where they hang a light fixture from the center too, or the recessed cans work too. You can also paint it an accent color.

justgotabme it's floor space below. The tile will change, but we will be leaving it open. Kitchen and breakfast area pic from the PO. The orb light is replacing the fan.

This post was edited by BergiesGirl on Mon, Nov 11, 13 at 13:36

Bergiea, another reason we went with the cans was because we have the stained glass hanging light over the breakfast room, a chandelier over the dining room table (open to the kitchen at the other end) and a ceiling fan on the family room side of the big counter area. Adding another hanging thing would have made me crazy.

ML

Thank you BergiesGirl. Since there's no island underneath I'd add cans inside the raise area or cover it and add cans.
One thing nice about can lighting is they now have LED bulbs that replace the old bulbs where you can see between them and the rims. The light and rim is all in one. We changed all our cans to LEDs like this:

justgotabme I had to look at that for a couple minutes before I got it. That is really neat, I take it that it really helps the lights just blend into the ceiling.

I tired to find the best view to show it all in hopes you'd be able to understand how they work.
I just found a video that shows how easy they are to install, though this one is slightly different than ours as they don't have the changeable magnetic trim. We actually prefer the white as it blends with the ceiling.
Ours look more like the thumbnail for the video sixth down on the right side of the page.

Here is a link that might be useful: Vidoe of instaling LED retrofit bulbs in can lights.