However, some times and places are more effective for establishing and strengthening our relationship with Allah. For example the Qur'an tells us the the night of Qadr is better than a thousand months in terms of its excellence for worshipping Allah. Similarly the ka'abah is a special place for communicating with Allah. Such differentiation is not a phenomenon limited solely to the spiritual world. The Qur'an instructs us to observe how date palms, despite drawing nourishment from one source (rain) , differ in that some grow from one root while others grow from diverse roots (in a V-shaped) [Surat al-Ra'ad 13), 4].
There are several reasons for why the Imams have specified certain times and/or locations for the recitation of some supplications:
1. In order to draw importance to reciting that particular dua. When someone knows something has to be recited in a particular time or place he/she is more likely to do it then just leaving it open ended.
2. They are helping us by informing us of the best things to say at these special times and places in order to benefit the most. This is a bit like a shopping list for someone who is walking through a store not knowing what to buy.
3. By specifying a time or place they encourage us to have the mentality and culture of doing dua and to incorporate this culture into our day-to-day routines.
Even though there might be a specific time and/or place specified for some duas, these duas can be recited at any time or place with the intention of "rajaa" (hope) that we should benefit from the reward that was promised to those who recite it at the specified time/place. This is as opposed to reciting the dua as an established action with a promised reward that has been identified by the Ahlul Bayt (a). For example you can make the intention that you are reciting so-and-so dua with the possibility that it is desirable in the eyes of Allah (swt) and that I will be rewarded for it, qurbatan ilallah.
With a request for your duas in this holy month.