Should the Marines earmark a brigade for eastern NATO? Good idea!
This article argues for a US Marine brigade for the Black Sea region. (subscription only)
I don't think the Black Sea region is appropriate. I just don't see us having missions there since a single brigade would quickly need to be reinforced by a lot more ground forces to survive let alone win. I don't see us trying to do that in that region.
I'd rather see the Marines go to the Baltic region. Although I'd like to see Marine aircraft in Romania where their naval focus could be used to threaten Russia's fleet from their new and improved home in Sevastopol, Crimea (occupied by Russia).
The ability to operate in the islands of the Baltic and to threaten the coastal flank of any Russian attack into the Baltic States would be helpful. I suggest Riga, Latvia.
One major factor for the Marines to consider in a NATO mission is that Marine efforts to get back to expeditionary roots to avoid being a "second Army" as they've functioned for pretty much every war we've fought since the latter stages of the Korean War is that the deployed Marines would need to heavy up.
Facing Russian mechanized forces, the Marines would need to bring heavy armor and mechanized mobility and firepower to any fight. If you fight an army, you need to be an army--whether you are the first or second one we have.