How do we determine when to use logic and reason in Buddhism? How do we better determine when it is time to use logic and reason and when it is a time to just see things as they are?

Note: We don't have to disclose the specific kind of meditation that we practice but it might make our answers less ambiguous -metta
It depends on what you want to abandon or negate. In general, there are two ways of negating (or abandoning) an object of negation. 


We oppose an affliction by way of generating a mind that is its opposite. For instance, a mind of love opposes a mind of anger... the virtuous intention to give (generosity) opposes miserliness... the wisdom of emptiness opposes ignorance (that is the mistaken conception of inherent existence)
We negate a non-existent object of negation by way of logic. For instance, we refute inherent existence  by way of applying logic, such as the reasoning of the diamond sliver, that of dependent-arising, etc.


Things are "organic" however. You can very well analyze death and impermanence so as to generate a consciousness in the entity of non-attachment, or of non-desire, or of renunciation, etc. According to Pabongka Rinpoche, once the mind of non-attachment has arisen (for instance), because it has found its way there through reasoning (and through paying attentions to things we usually overlook), there is no more need to apply logic anymore. We apply logic to find our way there again, and that way becomes easier to find every time we take it. Reasoning is just a means.

The reason we become angry without planning, "In five minutes, I will get angry" is that we are accustomed to it. We got there so many times in the past that our mind "naturally" takes the same course and find its way there again and again. When we are angry, even when we try to think "It's ridiculous and I am just telling myself stories, I am projecting, etc." we tend to think "Yes, but still... I have my reasons to be angry!" And we find ourselves reasons to be unhappy, we just feed it. The way we look at things and what we look at when we are angry are determined by anger. So, there is a need to apply logic to oppose this story telling by telling ourselves a story that is concordant with reality.

We have to do that until, one day, there will be no more need because loving kindness, compassion, generosity, etc. will manifest as naturally and effortlessly as our breathing goes. We will no longer get in our own way by thinking in a manner that lead us towards non-virtue.