As if there aren't enough confusing things to figure out in the military, each state has their own rules about the availability of unemployment benefits for spouses who have to give up their jobs to PCS with their active duty spouses. Thankfully, the National Conference of State Legislatures has put together a comprehensive list of states and their relative rules. It is concise and easy to read. Yeah!
Not so Yeah! is the fact that many states do not allow military spouses to claim unemployment if they leave their jobs to move with a military spouse. In those states, the loss of the job is considered voluntary and therefore ineligible for benefits. I know there is a lot of frustration about this, but I can see both sides of this argument. Clearly, it isn't really voluntary if your spouse is moving. However, paying benefits to military spouses who move is expensive for the state.
It's also expensive for the small businesses who pay the taxes that fund the unemployment payments. In most states, individual businesses are taxed based upon their unemployment claim record. It isn't really beneficial to a business to hire a military spouse if it is going to make their unemployment taxes go up when the service member is transferred. I can see how this would discourage businesses from hiring military spouses.
In general, you file your claim in the state where you last worked. If you worked in a different state than the state where you lived, or if you worked in multiple states, then your state Unemployment office should be able to help you figure out where to file.
You can read more at the Department of Labor's State Unemployment Insurance Benefits webpage.