How can I demo a website via an iPad?
It is quite difficult to convert VGA to HDMI because HDMI is digital, and VGA is analog.  It can be done, but the solution is often overpriced, and not worth it.  In my opinion, you should buy an HD projector, but if you can't then I would try something like AirServer and mirror it to your Mac and then connect your Mac to the projector.  Hope this helps!  In the meantime, I'll look for more solutions.



Update August 5, 2016:

Apple now sells a lightening to VGA adapter.