AFAIK you only need to use one upgrade "instrument" (like the 6,000 GP points) to upsell your room to one of the suites. At most hotels the suites have access to the Grand Club/Regency Club.
You can find the detailed info for each room category within the Hyatt website.
Go to the hotel of your choice
-> Rooms and suites
-> Click on the suite description
Should deliver something like that:
(Description of the entry level/smallest suite)
Text: "Access to Regency Club lounge included"
Or just ask the hotel where you will use the upselling instrument.
Hope this helps. And enjoy your stay.
Unfortunately this is not true in NA, there a suite does not include club access.