a Waterhog® runner. all the way over to the dog dish, in front of the bench.

lots of great colors and patterns to choose from.

https://www.llbean.com/llb/shop/506645?itemId=515470&attrValue_0=Olive&sku=1000199301&pla1=0&qs=3160526&gclsrc=aw.ds&gad_source=1&gad_campaignid=21715350398&gbraid=0AAAAADoqq1JNuLsBDGOb_dbjNxeGFuI_0amp;gclid=EAIaIQobChMIo9Wr4rK-lQMVGCnUAR2qwCOXEAQYBiABEgJrCfD_BwE&originalProduct=125892

With it being a busy area + a door to outside + dog it seems, maybe consider a wipeable vinyl floor cloth.

Thought this pattern would suit the feel of your room (comes in lots of sizes). I wouldn’t suggest a runner and maybe tape out a square and a rectangle to see what appeals to you.

https://therugdistrict.ca/products/spicher-and-company-vintage-vinyl-floorcloths-pattern-36-common-sense

Check out ruggable washable rugs/runners

https://ruggable.com/products/cyrus-rose-gold-tufted-rug

From what I can see, I like a rug size that fills the whole space around the bench. Looks like that would require about a 4'x10' rug? That size is not common. I used two overlapped 4'x6's to make this image. (These are jute, though; not recommended for areas exposed to moisture. Shown only to judge size.)

Great ideas already - fwiw I love the vinyl floor mats at hudson & vine

The area is small. it can fit 4’ x 8 at most so it has been a challenge. A bench may not be ideal but it is used. People still tend to hang in my small kitchen, even though I only have two counter stools. The bench is extra seating plus for taking off shoes.

With a dog you need washable and with wood floors something that does not transfer moisture to the floor . The bench seems overkill in size for such a small space but if you love it then the rug has to go all the way under it . A big must have for me would be a really good outdoor mat to catch most yuck and a sign that says wipe your feet please

Be cautious with the backing on whichever rug you decide upon. Vinyl and rubber backings have potential do damage the finish on your hardwood floors. I have a WaterHog outside and would like one inside but am paranoid about damage to floors. I've heard horror stories- and seen photos- of damage caused by ruggable rugs on wood. Natural rubber rug pads or felt/natural rubber are safe for your floor finish. Maybe a washable cotton rug (with pad underneath if you pick a color with any chance of dye transfer- dark or bright colors in weave). Sturbridge cotton rugs are nice and substantial weight, depending on colorways youre looking for. Hook & Loom sells washable cotton rugs and will send you samples for a nominal charge.