ID has OTC hunts for NRs, but several of the better areas do have that quota (or cap) to tag numbers mentioned above. First come, first served.
WY is a draw for all NRs, and the app deadline is Jan 31st.
NM is 100% draw for NRs (and residents alike) but one can go the landowner voucher route if they so choose, but that'll cost $$$.
Just some things to think about....