Looking at elk hunting in Utah this fall or next. What are the options for a public land non-guided hunt? What areas would be open for this? What licenses, fees etc. would be needed? yes, I know chances are slim this way but the country is incredibly beautiful out there and to walk it while looking for game would be well worth it even I didn't see a single critter.

I haven’t figured it out yet.  I’ve lived here for just over six years.  It’s a hell of a lot easier to hunt in GA.

You have missed the standard big game draw, it closed on April 25. Now your options are antler less draw that is open June 5-19. https://www.utah-hunt.com/

Over the counter Open Bull on sale July 11
Over the counter Spike on sale July 18

HuntinFool has decent info.

I'm in southern Utah and not real familiar with the northern units. Some units are better than others. Figure out a season that might work and I bet someone would point you in a good direction to have a chance at finding some animals.