"Taste" is to "flavor" as "touch" and "sight" are to what?

The sense verbs are an interesting paradigm. English has three types of sense verb (with a lot of overlap), and a number of derived nouns. Two of the verb classes differ in whether they're volitional, and the other one is an experiential sense with special "Flip" syntax.

One type of verb is the Non-Volitional: hear, see, smell, taste, touch/feel
Another is the Volitional: listen, look, smell, taste, touch/feel

Hearing: You listen to something on purpose, but you can hear it by accident.
Vision: You look at something on purpose, but you can see it by accident.
Verbs for the other three senses don't vary; you can smell, taste, or touch/feel on purpose or not.

The third type is the Flip verbs: sound, look, smell, taste, feel.
Again the three chemical/kinesthetic senses don't change in form,
though only feel works as a Flip verb:

That looks tasty / sounds flat / smells sour / tastes delicious / feels weird.

The subject of a Flip verb is not the experiencer, but rather whatever is causing the sensation being experienced. The experiencer is normally not mentioned, but if it is, it occurs in a preposition phrase (most likely to me).

Interestingly, only hearing — the sense used by language — gets to have 3 distinct sense verbs: hear, listen, and sound.

As far as nouns go, one can speak of a look and a sight (respectively from look and see), as well as a glimpse, a vision, an appearance, a sighting, an image — and no doubt many more — for vision alone. This is what a thesaurus is for.

Touch is underrepresented in nouns; adjectives are more likely. But one does speak of something having a feel, occasionally a feeling — a word which can be generalized to cover any metaphoric, psychological, or spiritual sensation, whether experienced or not, as in

I had a feeling he was going to betray us.

Besides already-mentioned feel (“A quality of an object experienced by touch”), feeling (“Sensation, particularly through the skin”), and texture (“The feel or shape of a surface or substance; the smoothness, roughness, softness, etc. of something”) (of which the latter is less applicable), consider the following.
• palpability, “The quality of being palpable”, that is, of being “capable of being touched, felt or handled; touchable, tangible”
• tactility, “The ability to feel pressure or pain through touch”

That word is sound. A flavor is what you taste, and aroma what you smell, and a sound is what you hear.

EDIT: Ok, after your edit, it now calls for something’s feel. Or again, its touch.

Touch/Feel the surface of an object. The sense of touch requires something physical and solid unlike smell and hearing and it is not interchangeable with feel which can also express a state of being as in "He feels lonely/hot/tired etc..." You cannot help but feel thirsty, hungry etc...

Touch is a deliberate action; feel can be both a voluntary and involuntary action. So you need a different noun from surface. May I suggest feel a sensation? And I prefer @John Lawler's see an image, or see a vision.

I think John's answer is pretty complete. In short, I'd say these are the two words you're looking for:

• see: look
• touch/feel: feel

The phrase "Look and feel" immediately comes to mind.

I may be biased by working in the software industry - I'm not sure if this phrase is actually more widespread, but I imagine it evolved the other way around with the industry picking it up because of its usage elsewhere.