There is a roughly 3/4 inch hole in my tile floor in the kitchen. I don't have any spare peices of tile, and I feel that finding a matching peice would be challenging. What's the best bet to patch and repair the hole?
Until you can find a matching tile, fill the hole with about anything that you can find. Even a wood plug. Look around the room to see if there is a tile that is under something that you may try to pull up and use. If the tile was properly installed, it will break when you try to remove it.
There are not a lot of options for this.
Handy Andy In Mt Airy NC
JB Weld. I'm using the Water Weld version to "fix" a chipped outside corner tile in my bathroom. The tile is 60 years old and impossible to replace, let alone match. I haven't even seen outside corner pieces like that for decades.
Or you could go for "interesting" and embed mosaic there. And I don't mean the stuff they sell in the big box stores on webbing. I mean actual mosaic in the older sense of the word, eg small bits of tile which are broken, randomly shaped, or purposefully shaped. There are videos on youtube showing you how to make your own mosaic pieces from salvaged plates and other china or take a "normal" new tile and use tile nippers on it to make small pieces for mosaic.