you didn't say if the slate is the same height as the tile will be. If it is, and depending on how it will look, you can tile straight up to it if you want. Only trouble is that often times this causes a major clash. If you don't like the marble idea (or have trouble finding it - the depots in my area only carry corrian strips, not marble) use a wood transition. If you stain it the right color, it can look REALLY good.
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