One additional, unsolicited piece of advice: try to check your bags in the same terminal from which your flight is departing to minimize the chance of it going missing / becoming delayed.

Although I rarely experience delayed baggage episodes-- both of the most recent experiences occurred when I checked bags at DFW's Terminal D when my flight was actually leaving from another terminal.

Obviously, this is anecdotal, but I suspect that AA's baggage handling system at DFW is set up to "expect" that people will check their baggage at the same terminal from which their flight is expected to depart, even though AA allows passengers to check baggage at any terminal.

Probably not a huge risk (I assume that most guests of the Grand Hyatt use the Terminal D baggage check facility, even if departing from other terminals), still....