Is there an olfactory equivalent expression to "the scenic route"?

Solution 1:

From the point of view of the dog, the scented route is appropriate. Scent, from Merriam Webster:

1 : effluvia from a substance that affect the sense of smell: such as a : an odor left by an animal on a surface passed over

b : a characteristic or particular odor especially : one that is agreeable.

The scented route also means that the dog is tracking the routes of other dogs and other animals. Dogs have been used for millennia to catch and follow the scent of an animal that is being hunted. Dogs now are specially trained to find a missing person, or to search for drugs in luggage at airports, or to find cadavers in places like Ground Zero. Some dogs are even being trained to detect the characteristic scents of various cancers.

The dog follows the odors on the scented route with enthusiasm, so we can safely infer that the scents are interesting, and probably pleasant, to the dog. In his turn, the dogs marks a tree or a hydrant, saying:

"Hi, I've been here".

However, From the point of view of you, or another person walking a dog, the odiferous route might be more appropriate, because, many of the things the dog is smelling with enjoyment would be repugnant to you. Odiferous, from The Free Dictionary:

Having or giving off an odor, especially a strong or unpleasant one: an odoriferous bag of garbage.

There may not be a word that perfectly captures both the dog's experience and yours on the same route, but the scented route comes close; you just find the scents disagreeable if you can smell them at all.

Solution 2:

Do you require something that specifically refers to where?  A phrase that captures the meaning you seem to be looking for is taking time to smell the roses.  It is typically used metaphorically / idiomatically:

Wiktionary:

stop and smell the roses
(idiomatic) To relax; to take time out of one's busy schedule to enjoy or appreciate the beauty of life.

The Free Dictionary:

stop and smell the roses
To become calm and reflect upon the finer or more enjoyable aspects of life, especially when one has become overworked or overly stressed.  You can't keep working these 80 hour workweeks, John!  You have to stop and smell the roses, or else what is all that work even for?

Urban Dictionary:

slow down and smell the roses
this means stop stressing out, overthinking, or complaining.  put your troubles in perspective and try to enjoy the short time you have on earth.

but there's no reason why you couldn't use it literally (or at least semi-literally).

TIL Ringo Starr sang a song called "Stop And Take The Time To Smell The Roses" (lyrics, video).  It's silly, and maybe a little subversive.

The phrase is also mentioned here on EL&U.