Matching Concrete to Tile Floor Height (1")
Level it... with more tile? 

I've done my share of concrete work, but there's no way I'd trust myself to float a finished floor and I wouldn't personally guarantee any work I did less than four inches thick. I'd tile it just like the rest, if I were set (haha) on doing concrete, I'd hire that out to a stone flooring specialist.

I doubt you own a commercial floor buffer and a 20amp grinder. Having only seen it done, I can't go into great detail. I just know that I don't want to grind on a floor for two days straight. IMO, tile is your best and cheapest answer: anyone can tile well enough and your labor is free.

Note: "Self-Leveling" is a name, not an adjective. Call it whatever you want: it doesn't. You still need to know how to float concrete and you'll still need a floor buffer to correct any mistakes.

Patching a slab so that you can tile over it is DiY. Installing a Stonhard floor is best left up to a professional company (of the same name, with which I've no affiliation but I did know some people that worked for them, who said the job sucked, but the dust completely coating the interior of their car told me that).