What is the word for a tactile satisfying feeling? Some examples include the feeling of magnets gently clicking together, the sound of a car door closing, or the feeling of pressing/clicking a really nice button.
a picture or sound that is crisp is clear [= sharp]:
Strongly built or made of strong materials; not flimsy or slender: a solid door with good, secure locks
Having a solid, almost unyielding surface or structure: the bed should be reasonably firm, but not too hard
Information Acquired Through Other Sensory Modalities
Human factors engineers work with other engineers in specialized functions such as acoustics and sound engineering; noise, vibrations, and harshness; and interior trim and materials to make sure that the vehicle provides the necessary cues of the right type and magnitude and enhances the pleasing perceptions (e.g., sound of the exhaust that conveys engine power, sound of door closing that provides the feeling of "solidness" or "solid build quality," tactile feedback received from "crisp" detent feel while operating electrical switches, smell of "genuine" leather from the seats).
Pleasant is a versatile word that also covers tactile pleasure.
Tactile has nothing to do with sounds, you get tactile pleasure when you touch something, and such a pleasure is available even for deaf people.
Tactile (Collins Dictionary)
of, relating to, affecting, or having a sense of touch a tactile organ, tactile stimuli
(rare) capable of being touched; tangible
Where sounds are concerned, here is a list, 'Pleasant, soft and gentle sounds' on Macmillan Dictionary.
'Pleasant to the Touch' article on The Scientist, which deals with touch-sensitive nerve fibers, may help.
Light pressure that excites C-tactile fibers produces a gentle, consistently pleasurable feeling.
frisson: a pleasurably intense stimulation of the feelings [merim-webster] (http://www.merriam-webster.com/thesaurus/frisson) Might be a little intense for what you mean, but I like it.
What the OP seeks to describe strikes me as the pleasurable and peculiar sensation or experience of “excellence” and “precision.” The experience is synesthetic, in general, and not merely or strictly tactile but also visual, aural, olfactory, and in some cases even gustatory.
excellence noun: the quality of being outstanding or extremely good. "the award for excellence in engineering"
synonyms: distinction, quality, superiority, brilliance see Google excellence
precision noun: the quality, condition, or fact of being exact and accurate. "the deal was planned and executed with military precision"
synonyms: exactness, exactitude, accuracy, correctness, preciseness see Google precision
Like one of the commenters, I don’t see the tactile connection with closing car doors (unless you’re talking about that little butt-bump that’s required when it doesn’t close all the way…that’s not entirely disagreeable), but I do see it with the magnets, that little pull just before they connect and click.
Anyway, one of my favorites is sliding my hand/arm under the backside of my pillow to discover/experience its coolness, which I find calming, comforting, soothing, and relaxing; any of which might also describe the feeling you get when clicking your magnets or rubbing your buttons.