Sure...so long as BOTH are permanent floors (tiles mortared/thinset into place and the hardwood glued/nailed/stapled/cleated into place). A HIGH END professional will be able to get this done. The tile setter will need to get together with the hardwood flooring installer to figure out the best form of transition (low-profile schluter, etc). It takes a bit of effort, plenty of coordination and +++SKILL (which you pay for by using the highest trained/priced profis you can find). It is do able. The price of the house will dictate how HARD you try to make this "transitionless".

Photos would help us help you boost them here in the comments

I can do that. I have that dark wood just about everywhere. I guess I was trying to break the wood up a bit. And, that photo where you're looking down stairs to the garage door, that's a direct walk way up to the kitchen area, so we walk it a lot with groceries and everything else coming and going. I was thinking tile for the durability.

We are replacing our tile floor in the kitchen and changing from 12x12 inch tiles set in a diamond pattern to 12x24 inch tiles set in a running pattern. Should the tile direction be opposite that of the wood floor of the dining room (like a T) or should it run in the same direction as the dining room floor (Note: dining room floor is 1930s variable width wood with widths ranging from 4 inches to 8ish inches and the ends of the variable wood planks butt up to the kitchen entrance.