OTC tags for critters with antlers in most places are a great way to meet other hunters. Colorado is a state that comes to mind. It is better than not hunting but you will certainly see a bunch of orange. East of the Mississippi does have OTC tags in some large National Forests with good hunting in states such as WV.
Cow elk on tags obtained through the draw is one of my favorite hunts. It is fairly easy to draw a tag in the Rocky Mountain states even in the premium units that produce great bulls. Of course fate will let you see huge bulls when all you have is a cow tag, but cows taste better anyway. Cow elk, doe deer, doe pronghorn, etc. let a fellow hunt the same country as the trophy buck/bull hunters but most fellows will not travel far to hunt them.