Check out the Walker Zanger online catalog. Amazing choices of porcelain tile trims, from Old World to contemporary. A narrow strip might be more durable than wood.

I prefer to stop the tile in the kitchen/nook. The hardwood can then flow from the formal dining area down the steps and into the living space. The ONLY thing that would cause any concerns would be the ability to find MATCHING stair treads for the hardwood you choose. Sometimes this is a BIG problem...if that is the case, then moving the tile all the way into the dining area would be the way around it. But you have to find this out BEFORE you choose/order your flooring. You do NOT want to make this decision on the fly...only to find out that you cannot find more of the tile in the same dye lot...that's WORSE than having miss-matched treads. Much, much worse. All of these decisions/questions MUST be answered WELL before you put pen to paper. A designer who is well connected in the building industry would be able to do all the leg work for you - without much effort. S/He would have already run into these issues DOZENS of times in their career and will know the ins and outs of working around these issues. And s/he will have ALL the needed professionals on speed dial. Which then becomes the NEXT dilemma which MUST BE dealt with before pen is put to paper. Whew! Lots of things to do before anything is decided. A well versed designer can be worth his/her weight in GOLD at this point.

It needs to be flat not necessarily level. If it is not prepped and flat you very well may end up with cracked broken tile over time.

agree with @millworkman or get a piece of marble threshold at your local home improvement store... in anycase, you will need a carpenter with tools and skills!