that looks like vinyl or linoleum are you sure it is tile??

Ya, it's not pretty, but definitely tile

I would cut the tile back to where it is already cut out. Create a rectangle with the wood floor and door frame. Then use an accent tile to create a transition! Good luck

I would fill in the gaps and cover with a nice ceramic looking vinyl tile that can be put down over existing floor.

A floating floor, such as cork or vinyl can go down over top for a quick fix/pick-me-up. You will loose a little floor height...but not much.

The option to run a border (a nice mocha would look great with the darker floor in the hall) will do the most for the least.

Linda has a good idea. We actually found left over tile in the garage storage when we bought this old house. Check those dark corners in cabinets. Use small scale accent tiles to create a border or "rug" if you can't find original tile replacements.