Re: This has to be simple.
Take the average latitude of all the participants, and the average longitude, and then find a location near that lat/long
with decent accomodations, nearness to major highways or airports, or fun things to do.
Don't be afraid to subjectively take into account things like potential bad weather, bad roads, etc to modify your decision.
You could probably do just as good a job by just looking at a road map and eyeballing it, your experience and intuition will automatically factor in stuff like "ugly mountain pass in winter", or "this is just a short hop to Vegas!!!!".