Modern open-source tools for simulation of NMR spectra
In Org Biomol Chem 2016, 14, 3943, Goodman reports the replacement of some "tradition" (expensive) programs with free/open-source ones, as applied to their dp4 method. 

Specifically:


Molecular mechanics with tinker (I believe as a replacement for MacroModel), you may or may not want this step depending on what you're doing. The paper is looking at molecules with stereocentres and as such, they appear to have wanted to ensure the NMR values calculated matched the most likely conformation of the molecule experimentally studied. 
NMR prediction using NWChem (replacing Jaguar as the gold standard) to do the DFT calculations. There is some mention that this was slower, but again, it would depend on what you're interested in studying. 


I think that fulfils your requirement for being able to do the prediction using open-source programs. 

As for scripting, there is a mention in the paper of wrapping the whole thing up in a python script (and to my knowledge, there isn't actually a GUI for either piece of the aforementioned programs), so it should be amenable to this. 

One thing that it doesn't appear to do, is to graphically plot the resulting data generated (I believe they just compare a list of values to a list of experimental values), but you should be able to plot this in something like MatLab, or, if you play enough, it should be importable into TopSpin via something to turn it into a set of suitably written values.