I know this seems pretty vague as an answer, but most any unit in western Wyoming would have lots of public land and good numbers of elk. Probably depends upon your ability to get around in the mountains.
The general WY elk tag is probably has the best "easy of drawing to quality" ratio of any elk tag in the country. Look for the units with the worst odds, and those will probably be the units with the best combination of quality and public access.
Easiest to draw units usually have some access issues.
I know that is not very precise, but I think you will find ample public ground in any unit west of I-25, with very few exceptions of the units closest to I-25.