What type of coffee maker creates the most coffee scent? I stopped drinking coffee for a while but recently picked it back up, mainly because I enjoy the scent.  Previously I had a Keurig machine; convenient, but produces almost no smell during brewing.  Until I broke it a couple days ago, I was trying out a french press.  Again, very little of that heavenly wakeup scent.

What method of coffee making will best fill the house with coffee scent?
If you want a lot of scent, you will want to make sure that nothing stops evaporation - so no lid and a large surface area are paramount.

The classic method would be hand-filtered pour-over, which system you choose is up to you, famous examples are Melitta, Chemex or Hario (which all follow the same principle). And as an additional benefit you get to enjoy the aroma right there while you are brewing the coffee.

An alternative could be Turkish mocca, where super-fine grounds are boiled. The boiling process will likely create more steam, on the other hand, the surface area of a cezve is a lot smaller than that of a filter. You will also have a quite different end product and have to decide for yourself whether that fits your expectation or not. 

And in any case, I recommend grinding your beans fresh just before brewing, you’ll be surprised at how much of a difference that alone will be. And grinding also releases the coffee smell you are aiming for.