Time resolution of the Short Time Fourier Transform (STFT)
There is no single "time instant" associated with a short-time Fourier transform. As you noted, if you perform a DFT on data collected from $t = 0$ to $t = 64$, then there isn't a single point in time that you can associate with the output from that DFT; it is a function of every sample in its time interval. 

For this reason, there is no standard convention for how you might denote the time axis associated with successive STFTs, if you were tiling them together into a spectrogram, for example. You'll just need to pick a convention that is meaningful for your application. You've already identified a couple reasonable ones (using the beginning or center of the DFT's window as its "time instant").