You should definately look into applying for a 1st season rifle elk tag. Many of them are either sex and can be drawn with 0 points. If you don't draw, then you can get the tag the next year for sure. You could then hunt the unit in the second season to get familar with the unit. But the 1st rifle is king for elk for several reasons. They are generally still in rut, no deer hunters, and limited tags (no OTC).
As far as a recommendation for a specific unit: Any unit in the western 1/2 of the state will generally hold elk. Look at the link provided in an earlier post and specifically for two stats: How many points to draw and hunter success. Find a unit that can be drawn with 0-1 points with good hunter success and you have probably found a good spot to go. Then check and find out for sure that it has plenty of public land.
If you want some general areas that you can get away from roads where there are elk: Flat tops wilderness, maroon bells wilderness, west elk wilderness, wimenuche wilderness, san juan wilderness, Holy Cross wilderness.....
Here is a link:
http://www.coloradowilderness.com/wildpages/map.html