Is there any way to alter the graphics of the SNES so that they don't appear grainy on my HDTV? Different cables, different wiring, etc? I'm currently using an RF cable. Ideas?
Natively, yes you have options depending on your model SNES and TV. Your best bet is S-Video, as that is the most common plug available, but optimal is RGB but that isn't typically supported on modern TVs.
The option you are using actually provides the worst image possible, but all of these will look bad on a HDTV, due to the way it upscales. Your better options are an external upscaler (Which is expensive), a CRT (Super clunky), or emulation.
The most effective option I have found without a having to spend around $600 or lugging a CRT into the lounge room is the Retron 5. It's light weight, uses original cartridges and controllers and upscales to HDMI. However, it is an emulation machine, and it isn't quite the same as playing on original hardware.
There is this option as well: SNES Component cable. I haven't actually seen these in action however, so research is advised.
A great site for information about getting retro consoles working in a modern environment is Retro RGB. Most of this information is from that, with a bit of personal preference from Youtube videos.