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There aren't any decent areas open on the eastside for late muzzleloader. With that tag, you need to focus only on the early season. Save your money and wait till next year is my advice.
I took a look at the open GMU's. I am not sure if you are forced to hunt either western or eastern WA, but assuming you can only hunt the eastside; I would take a look at GMU 373, 379, or specifically 381. I have seen alot of guys on this forum speak well about these areas. They have posted some nice pic's as well. I have never hunted there, but I have heard nothing but good things.I have only seen a small number of elk in and around the Steptoe area when I have hunted in and around the GMU. It is usually fairly weather dependent. The elk are there year round, but the population and success rate goes up if the area gets heavy snow. I would mabe take a look at the far eastside of Steptoe on the border of Idaho. I have a spent a fair amount of time hunting there, and the GMU will get elk migrating over from Idaho and out of the Blue Mtn.s Cheney is a great area for elk year round, because they elk move in and out of the Turnbull Wildlife Conservation Area. The issue is land access. I spent some time hunting all around the area, but access can be tuff. There are some areas open to the public, which you may be able to take advantage of. I would stay away from north central eastern wa, unless you know where a specific herd are located. My family owns a hunting and fishing resort up near Tonasket. The elk are there, but it seems very spoty. I don't know all the GMU open that well thou.
There aren't any decent units open for late muzzleloader. If you want to hunt late muzzleloader you need a west side tag.
Yup, no real good options for muzzy hunters on the ES for late season. Not sure why the WDFW keeps on the muzzy hunters.. Used to be some good seasons.