Meaning of "has a ____ to it"

Solution 1:

I would say that adding to it emphasizes perception of the thing, as opposed to an inherent quality of the thing. In other words, it emphasizes or draws attention to a subject that observes or otherwise perceives or interacts with the thing.

The expression really refers to an effect on the observer. In a nice ring to it the ring[ing] is not a quality of the thing but a feeling/thought that takes place in the observer.

Solution 2:

It is a good question.
The have X to it construction reminds me of some constructions in other languages.

• Spanish A mí no me gusta el cilantro. 'I don't like cilantro'
  [literally To me not me likes the cilantro.]

Spanish has no transitive verb like, with the emotional perceiver as subject and perceived thing as object; instead, there is a flipped construction with gustar, which takes the perceiver (me) as object, and the perceived thing as subject. Adding a mí is optional and emphatic.

• German Er hat sich die Hände gewaschen. 'He washed his hands'
  [literally He has to himself the hands washed.
  Sich is the 3p dative-accusative reflexive pronoun]

German prohibits using some inalienably possessed body parts and other special terms as objects with possesors. Instead, there is a reflexive dative construction, converting 'wash' into a verb with an indirect object.

In both of these constructions, there is a repetition of some NP, for some kind of pragmatic purpose like emphasis or taboo; and at least one of these NPs is typically a pronoun, just like the have X to it constructions.

This suggests to me that the to it construction (which doesn't have any common name I'm familiar with and doesn't seem to be in the literature yet) may be a work-around idiom for some deficiency in English. Which in turn suggests looking for how one says this in other languages.

And looking for other verbs than have (or give, which involves have) to try it with:

• That has/gives a nice color to it.
• *That paints a nice color to it
• *That looks like a nice color to it
• *It/That seems a nice color to it
• *She wants a nice color to it

And looking for other subject-object relations to try it with:

• That has (quite) a kick/a smooth feel/an interesting rhythm to it.
• That has a top/a bottom/a door/a latch/4 sides/a real future to it.
• *That has a steering wheel/new tires/an overhaul to it
• *That has a missile launcher/a machine gun/armament to it
• *That has my approval/his authorization/a license to it

Solution 3:

I would suggest that when expressing something with "has a ___ to it" there is an implied sense of what the word "aura" means.

the ideas of "radiating" or "emanating" a "feeling"

A few definitions of "aura" might help.

aura at Merriam Webster

1 a : a distinctive atmosphere surrounding a given source

The place had an aura of mystery.

b : a subtle sensory stimulus (such as an aroma)

and

aura at Dictionary.com

1. a distinctive and pervasive quality or character; air; atmosphere:

an aura of respectability; an aura of friendliness.

2. a subtly pervasive quality or atmosphere seen as emanating from a person, place, or thing.

Solution 4:

The way I use 'a has b to it' is as to express that there is a sense/feeling of b in a. For example, to me, 'the movie has a strong vibe to it' says that there is a sense of a 'strong vibe' in the movie. As to your example, 'it has a nice ring to it' is effectively saying, 'there is a feeling of a nice ring in it'.

At other times, such as your example 'it will have a nice colour to it' or the sentence 'this football player has got nice feet to him', the to it part may stand for aspect instead of sense/feeling, so 'there is an aspect of nice colour in it', and 'there is an aspect of having great feet in this football player'.

P.S. In fact, having thought about it, the sentence 'it has a nice ring to it' may refer to either case depending on the context. For example, 'this phone has a nice ring to it' will probably fall into the second group.