which mac mini are you running? are you running it to a receiver or just to your tv? does your tv have vga inputs?
if you have VGA on your tv id say run VGA from the mini. itll cost alot cheaper for cabling and will also help avoid possible resolution issues. also if you needed audio there are a bunch of cables available on amazon that have VGA bundled with 1/8" so you would only have to run one cable with both video and audio instead of two separate.
as for HDMI runs.. i believe the max run before signal loss would be about 50" so you should be ok -- but each situation varies. I work in concert production and run about 150" vga for the video before it needs a video amplifier to avoid signal loss.
if you are worried about it being in sync, i do not see too much of a problem since you don't have much processing to go through, however, that long of a run with a 1/8" makes it more vulnerable to RF freqs. and what not (like when a cell phone goes off near a speaker, etc). but not knowing your full set up, running the 1/8" might be your only option.
are you sure there isnt a way you can make the mac mini move closer to your tv?