I'd consider removing the base cabinets and doing the job correctly - which is to do the complete floor including under the cabinets. Failing that, as others have said, you remove the toekicks, extend the new tiling under the cabinets past the point of where the toekick was, then cut the toekicks to the new height required if the new floor is taller than the old. If the new floor is thinner than the old, the toekicks would be too short and would either need to be replaced or augmented with a shoemolding such as a 1/4 round - same as you'd do with baseboards on a hardwood floor. Bottom line is the toekick sits on top of the new floor and is cut to fit. If the new floor is very irregular like a travertine or natural stone then you'll end up with gaps of course in some points but that's part of the deal with irregular flooring.

It's funny to read this thread from 5 years ago hearing people talking about travertine as dated. My wife and I just bought a house and it is a pretty big upgrade to go from the included tile backsplash to a travertine backsplash. I guess my point is, and I doubt anyone is even reading this anyway 5 years later, but my point is that I agree with the people that say go with what you like and don't worry about anyone else's opinions. It's your house. Why do people always concern themselves with how other people will like their things, when they are not the ones spending all their time there.

I had honed Travertine in a previous home and loved the appearance, but even with sealers, it can stain if you are not religious about addressing marks immediately. Drop a berry and in 5 minutes you'll have a stain that will take some time to address. I'm sure you know it costs more to install than regular tile. Still love the appearance and so when I moved to Florida, I installed a porcelain tile designed to look like Travertine. Unless I tell visitors, they assume it Travertine. Much easier to maintain, cheaper to buy and cheaper to install. Now you can have a larger format tile. These below are 24 x 48 tiles.

Second consideration - how long to you expect to live in your home? Most home owners own 3 homes in their lifetime. In 2022 the average tenure of homeownership is 13.2 years. No one owns the same home for 150 years, so it doesn't really matter if the flooring will last that long. You have to weigh many factors to determine the best use of your money. Initial cost, cost of maintenance, ease of maintenance, personal preference, return on investment and competing priorities. If I spend an additional $10 k on flooring and plan on moving in 10 years that flooring cost me $1000 per year. If I spent that same money on paying down my mortgage how much would I save on interest? If I invested that money in high quality furniture, that furniture can go with me to my next home. If I invested that money in my education I can increase my earning potential for the rest of my life. If I am not all that into the look of the floors in my home, but love traveling and seeing the world that $10 k may be much better spent on a trip to Europe or South America or an African Safari. My priorities when choosing a flooring for my home were: 1. Dog friendly 2. Easily maintained 3. Easy on old joints and bones 4. 20 year lifespan Without considering cost hardwood, carpet, tile and stone failed one or more of my requirements. Personal preference - I prefer the look of tile over wood. Had a home with tile for 20 years and loved the look. Grew up in farm country where most 100+ year old homes had hard wood floors and that is what comes to my mind when I see hard wood floors. Perfect for an old farmhouse. Not what I envision for my MCM rambling ranch. Other consideration was the use of area rugs. Almost everyone I know that has hard wood covers 80% of the floor with area rugs (mostly to protect the floor). I wanted to avoid carpet especially knowing that I may end up using a walker in the next decade or two.