Do you know what kind of tile it is? if so, you might try the website below. They have alot of discontinued colors from several different companies: Here is a link that might be useful: This Old Tile

So....the only room on the first floor with hardwood right now is the den? You can put hardwood throughout and refinish the den in the process, everything will match downstairs and you can get it close enough no one will notice if it's slightly different on a different floor. No to engineered flooring if you want to try this. Why is someone suggesting oak of a different plank width than what you currently have? Odd. golden oak finish is pretty neutral. better to have the whole house match than to have one level trendy and one level classic. functionally it sounds like the materials were well chosen- carpet for a play room, tile for an entry and powder room...could be just a personal design choice. Pictures would help.

I'm sorry but the only option (to get what you want) is to sand and refinish ALL of it at once. If you had planned on that in the first place, your flooring professionals would have matched the species and the cut and the grade of floor. They also would have matched the THICKNESS of the planks. Or ideally they would have told you how it was going to turn out...and that the best option = remove the old and lay all the same floor. It is CHEAPER than doing a sand/refinish on Aluminium Oxide floors for the TOTAL square footage. Sigh. I think you have TWO different species of wood. You certainly have two different GRADES of wood (the new one has ++++ plank variation and HEAVY grain presentation. This tells me that if you sand all of this down you will STILL have two floors that look VERY different...even with the same stain. Right now my 'fix' = remove the old wood in the entrance/foyer. Use the entrances to the other rooms as the 'break'. Use the edge of the new wood as the break. Now you drop in stone or porcelain or vinyl that LOOKS like vinyl or porcelain. By removing the SMALL amount of old wood in the entrance you will REMOVE the eye sore that is 'mismatched' wood floors touching one another. It will do the 'most for the least'. Removing the old wood and prepping the subfloor = $2/sf. New stone-look vinyl tiles = $4/sf. Cost of install = $3/sf. Total cost of job = $9/sf. Size of the job? Looks to be about 100sf = $900 and you have a BEAUTIFUL foyer without ANYONE noticing the two woods are not the 'same'. It is the simplest, easiest way to fix this without messing around with sand/refinishing wood that shouldn't be touching one another anyways.

It's really hard to give advice without pictures...the safest options would be to match the tiles or use carpet again.