There are a lot of good elk units here in AZ. Obviously the few real trophy units, but even the "lesser" units all hold good bulls and are easier to draw. The late rifle hunts are also a little easier to draw than the early archery hunts. As for specific units, you can't really go wrong just choosing one between 3 and 8.
Know the draw! AZ goes on a bonus point system where every year you put in and are unsuccessful, you get a bonus point. You also get an extra bonus point if you put in for 5 consecutive years and another if you take the Hunter Safety Course. A bonus point essentially gives you an extra number, similar to having an extra raffle ticket. So when you put in the first time, you are going to be assigned one random number...whereas, I currently have 5 bonus points, so I'll be assigned 6 random numbers. The Non-res rule is that only 10% of the tags for any hunt can go to non-residents in which up to 5% of those tags may go in the bonus pass. The draw goes in 3 phases, in which only the first 2 really matter for elk. The first phase is the bonus pass. 20% of the tags for every hunt are set aside for the applicants with the most bonus points. For example, if there are 100 tags for a specific hunt, 20 tags will be given out in the bonus pass, of which up to 5 may go to non-residents...which just about always happens for these hunts. The second phase of the draw is called the 1-2 pass. They just start with number 1 and go right down the list. When they get to your number, if your 1st choice still has tags, then you get drawn. If not, they go to your 2nd choice and if it still has tags, then you get drawn for that. If your 1st and 2nd choices are gone, then your number gets set aside for the 3-5 pass, which works the same way as the 1-2 pass but there are rarely bull tags left for. So in the example above, 20 of the 100 tags are given out in the bonus pass and 80 are given out in the 1-2 pass, of which the other 5 can go to non-residents. Hopefully that makes sense.
It might be worth going to the AZ Game and Fish Website, click on hunting, scroll to the bottom of the page and click on bonus point reports. You can figure out how long it would take until you would be guaranteed a tag. For example, the late general hunt in Unit 4B had 150 total tags last year, 30 of which would go in the bonus pass. 10% can go to non-res, so 7 could go in bonus pass (no more than 5% of the total tags). So if you look at the report for the unit, 1 person drew with 10 points (probably a non-res) and 6 drew with 7 points (probably the remaining non-res tags). The other 23 bonus point tags went to most likely residents with 5-6 points. So, if you hit 7-8 points for that unit, you could be almost guaranteed a tag for that unit.
Sorry such a long post, but once I started typing, I just kept going...haha.