We are a medium-sized academic research lab whose main outputs are new statistical methods for analyzing large datasets. We generally develop in R and MATLAB/Octave.
We
For R and Python integration you might also want to have a look at
I've been looking for something similar - simple rapid GUI in R. It seems there's a new alternative from RStudio guys.
Shiny should be sufficient for small web interfaces without much coding. Seems like a viable option if you need a simple input/output style of UI.
Why not continue to develop directly in R? There are a number of packages that allow you to develop GUIs (gWidgets RGtk, tcl/tk, RQt, Rwxwidgets, rjava) or web applications.
I'd go with Python and PyQt4 for the UI, and use Rpy to interface to R.
There's the QtDesigner for interface designing and you can generate python from that. QtAssistant gives you a fully hyperlinked documentation set for Qt which is the best I've ever used.
Well worth it!
I haven't tried directly connecting Octave with Python beyond setting up Octave apps as a server and having a Python client call in, but I've had some luck integrating R with Python courtesy RPy. In some of our applications we build e.g. a wxPython + matplotlib Python frontend, and call the R scripts directly through RPy.
You might try looking at RedR, which lets you wrap R packages in a Python GUI.