My first recommendation is to go to each Elk state's G&F web sites (New Mexico, Colorado, Wyoming, Idaho, Montana, etc.) and read as much as you can about license prices, general regs, season date(s), drawing or over-the-counter, drawing odds, elk sucess rates by area, public access lands or not, etc. I'll tell you this, I know Wyoming for insatance is a drwaing only state for non residents and the drawing application dates are January 1 - 31. So you'd have to decide soon if a state is drawing only.
As far as "Where to hunt on public lands"? . . . there are billions of square miles (NOT ACRES) of public land out in the west. BLM, state trust lands, National Forests, and public assess lands (private land that public hunting is allowed on). A company called DeLorme makes an atlas for each state that shows pretty good details like property ownership and topo info. You may also contact the BLM office in your area or each state and see if they offer a wall map of the state. Mine is about 3' X 5' and shows at a glance property ownership (private is whit, state is blue, BLM is gold, and Nat'l For is in green).
Narrow down your end location/state/region according to the abovesubjects, then get more specific advice later.


If you want to know how to hunt elk. . . forgetabowdit!