Does anyone hunt in Utah? Some friends and I are thinking about going next year for an antlerless/spike Elk, and a mule deer. We can get the tags over the counter...

I haven't hunted yet in UT, but plan on going next year. I still need to find someone with some good hunting property that will let me hunt there. Do you know anyone?

No, it will be public land where we will go.

Yes you can buy Buck Deer and Spike Elk tags over the counter.
But anterless tags are a draw.
Most Southern Utah deer tags are on a lottery systems. There are never any tags left over after the draw.
Some Northern Utah tags can be bought over the counter, But most units they sell out long before the hunt.

If you think you can show up and buy tags the day before the hunt, You will be very sorry.

70% of Utah is public lands. So access isn't so much a problem as knowing where to go. Elk in particular move away from the roads and hunting pressure as the season opens.
Most private land is now run as a CWMU where land owners sell tags at high prices.