You didn't say what your elk hunting goals are or even what kind of hunt -- bow, muzzle-loader, rifle -- you are doing. If your goals are just to take any elk -- cow elk, any legal bull -- I don't know that switching areas is your best strategy. Most advice I see suggests that sticking to one area and learning to hunt that area well is your best strategy. Of course, your area needs to have elk in it, but presuming your area has elk in it, just going to another unit that also has elk in it throws away the opportunity to leverage what you have learned from experience in your unsuccessful hunts.

I don't know how you are hunting, but a good strategy for you to consider is hooking up with one or more experienced elk hunters and joining their elk camp. If you pay your own way and carry your own weight performing chores and you aren't extremely obnoxious or otherwise socially repulsive, chances are you can find some elk hunters to take you under their wing. This is a way to jump start that experience thing I talk about in paragraph 1 above.

Another thing to consider is going to your area and scouting it before the elk season. Go spend 5 days to a week in your elk hunting area in late August or even in mid-September and try to find where the elk eat, where they bed, how they get between these places. I know this is difficult to do for people with limited vacation time, but it helps reduce the number of years you have to come up empty, paying your dues as it were, before you figure out an elk hunting area and start harvesting elk. This is an alternative if you don't like the idea of joining forces with an experienced elk hunting group.