Free nights are valid at any property - we believe it comes from the same inventory as regular points award nights which is the same inventory as the "base entry" room for the property - so you can get it on awards if the "base entry" room is available for revenue booking. You should be fine for Moscow for TSAR since you're way out for now (and it was available last week when I exchanged emails with Doug).

Like I said, I know too much about the Hyatt program - more than many of their Customer Service Reps.