First of all, feel free to think of it however you want, as long as it helps you understand how the sentence works. Secondly, this may not be a question with an objective answer. What follows are several considerations concerning the structure of 飲むのに良い場所だ, shortened for briefness' sake.
【A】→【B】 means that B is modified by A.
To address one of your concerns, i-adjectives cannot be modified by a 連体形-clause the way a noun can be modified. Thus, a sentence like *【酒を飲む→良い】→【場所だ】 is wrong, you need the particle(s) のに. However, it can be parsed as 【酒を飲む】→【良い→場所だ】, with 飲む modifying 場所, but it means something different: A great place, where one drinks Sake.
We could translate the sentence as A place that is great for drinking, which we could choose to interpret either as (A place that is great.)(For drinking.) or equally plausibly as (A place that is:)(Great for drinking.)
In a sense, many particles work like grammatical cases (or some prepositions) in that they establish the relationship of a noun to the sentence. So for drinking marks drinking as the goal of the sentence's verb action; and that is how I think about するのに甲だ.