No, a will does not have to be filed in any courthouse. Real estate deeds of trust, however, need to be recorded, but not wills. Also, do not put your will inside a safe deposit box.
There is nothing wrong with appointing your spouse as executor, but I generally do not counsel that since there is always the chance that both of you die in the same accident. One way is to have you appoint your spouse in your will, and your spouse appoint Uncle Elroy in her will.
Draft one soon while you are thinking about it.