If you were to do a tile rug, I'd want it to look like a rug, not like a pristine white backsplash -- that would wreck the illusion, be difficult to keep clean, and threaten to make your kitchen feel like a bathroom. Either get a mosaic, or go with eash-to-launder rugs (or a comfort mat, which just needs wiping off). https://www.amazon.com/Imprint-Cumulus9-Dove-Runner-Kitchen/dp/B0764NW2BH/ref=sr_1_3?ie=UTF8&qid=1519925497&sr=8-3&keywords=comfort+mat+dove

I would steer clear of wool, too. As hard wearing as wool is, kitchens are sloppy places so make your life easier. I have a washable cotton rug from Hook & Loom in my kitchen. It's between my stove and my sink so it gets plenty of abuse. I have washed it at least a dozen times, colors have not changed and there's not a loose thread on it anywhere.

Wendy, Your kitchen would look great with a runner or more of that full room look. For the full room you may have to put 2 together to make the full length of you kitchen. Wasn't sure the other colors and style you are looking for but some examples below. the blue full room one not shown in the room is an example of one you can do that doesn't have a border so 2 together can look seem less as one rug. You can sew or use carpet tape to keep them together. lots of other patterns colors and styles you van do this with just as long as it looks seem less from one to the other. You will probably have to trimmed off the adjoining ends to put them together. If rugs.com has the right sizing to the picture, a 4'11x 6 would be about perfect to double but you should measure to confirm.

We have two Roombas - the i7+ that empties itself and the 980 which is a few years old. Both are fantastic on our hardwood floors. I love how the i7+ empties itself. Both have rubber rollers so they aren't going to scratch the floors. If you have any area rugs that shed, I will say the i7+ sometimes leaves behind a few clumps of rug fuzz it has pulled up but not made into the dust bin. Apparently, this is a common issue with the i7+ so I'm not sure if it's been rectified with the new j7+. I've never had that problem with the 980 when used on the same rug. For us, it's only on one of our large area rugs that has been a shedder since we bought it. I would buy one again if either broke. They're very convenient to help with our shedding dog. I just saw on Prime Day that the i7+ is 50% off today at $499. I bought it on Prime Day last year with the same pricing.