An ounce of preparation is worth a pound of cure
I almost always email the hotel, about a week prior to a stay. The subject of the email is "(my last name) arriving (date) for (x) nights".
The email tells them what time I'll arrive, what time I'll depart, and room preferences.
"Last year you put me in a room overlooking the city, which was fantastic. A similar view would be appreciated this year."
or
"Concerning the specific room assignment, a good night's sleep is very important on this trip, so please find me a quite room. Thanks."
or
"Although I choose NOT to use one of my Suite Upgrades on this trip, I would welcome a comp upgrade based on Hyatt's policy of upgrading Globalists to the best available room including suites."
or
"I'm writing because Globalists get upgraded to the best available room at checkin. However, I will check in VERY late (past midnight). Therefore, please assign me to the best possible room BEFORE I check in. Thanks".
Like so many others, I resent having to cajole the front desk into providing my earned benefits. I much prefer to cajole them by email, well in advance of the trip. In an ideal world, the Globalist upgrades to "best available room" would be automatic and assured. In the real world, you kinda hafta ask.
Specific to the Original Poster, you get 4 suite upgrades for making Globalist. Then you can get 1 more at 70, then 80, then 90, then 100 nights. So you can end up with 8 per year.