With any transition you’re still going to need to replace the broken tile. I would use a wide custom solid wood transition beveled and trimmed to lay flat when installed. Stained in a color that works in the space you could also do your trim in the same wood and stain.

Another option: when we added saltillo tiles to our front walkway, it made the walkway about a half inch higher than the driveway. We had purchased decorative tiles to place vertically on the step up to the porch, but the step-up was too shallow. We used them as a transition to the driveway, a gentle 1/2 inch slope. It has been about 10 years, none have cracked or loosened. Obviously, this is less subtle than Kate's suggestion of a stained wood piece (a great idea), but it goes well with our Spanish tile roof and saltillo walkway and porch. Just another possible solution.