RE: Public Land
Not sure what you have in mind but there are very few places a nonresident can hunt moose without a guide. The best bet for Elk I think would be Colorado. Over the counter tags and a great elk population. The trophy quality leaves a lot to be disired if that is what you are after. I am not a trophy hunter so I love hunting Colorado. If you can draw a tag for New Mexico or Arizona the chances of getting a trophy is much better.
You can get on the Colorado Division of Wildlife site and they have a section on elk densities and harvest numbers. This would be a good place to start. Give them a call and they are usually pretty good to talk to and will give you pointers on area where the elk are.
Good Luck. Once you go you better be prepared to go again because it is addictive!!
WW