I assume that you were a Hyatt Platinum when you got the card, right?
Plats get 2 free nights plus 2 free suite upgrade certs (for up to 7 days each).
Short answer: the suite certs are only good on paid nights.

Here are the terms and conditions (I've bolded the suite cert T&C for Plats):

GOLD/NEW MEMBERS:
You will qualify for and receive your two Hyatt Gold Passport® Free Night Awards after your first purchase. First purchase does not include using your account for balance transfers or cash advances, or using any checks that access your account. Each Free Night Award is valid for use for one (1) night in any available standard room within one year from issuance at any Hyatt Hotel or Resort worldwide. Awards are not transferable. After qualifying, please allow 10 days for your Free Night Award(s) to post to your Hyatt Gold Passport account. For complete terms and conditions of the Hyatt Gold Passport program including the use of Free Night Awards, see goldpassport.com. This one-time bonus offer is valid only for first-time Hyatt Card cardmembers with new accounts. Previous and existing Hyatt Card cardmembers/accounts are not eligible for this bonus offer. Chase is not responsible for offer fulfillment. If your account is not open for at least 3 months, Hyatt and Chase reserve the right to deduct the Free Night Awards from your Hyatt Gold Passport account. Annual fee applies. For pricing details, please see Pricing & Terms.

PLATINUM MEMBERS:
To be eligible for this bonus offer, you must be an existing Hyatt Gold Passport Platinum member at the time of application. You will qualify for and receive your two Hyatt Gold Passport® Free Night Awards and two Suite Upgrade Awards after your first purchase. First purchase does not include using your account for balance transfers or cash advances, or using any checks that access your account. Each Free Night Award is valid for use for one (1) night in any available standard room within one year from issuance at any Hyatt Hotel or Resort worldwide. Suite Upgrade Awards are valid for use within one year from issuance on paid nights, each for one stay of a maximum of 7 consecutive nights, at participating Hyatt Hotels and Resorts where suite accommodations are available. Suite Upgrade Awards are not available on all suite types. Awards cannot be combined. Awards are not transferable. After qualifying, please allow 10 days for your Awards to post to your Hyatt Gold Passport account. For complete terms and conditions of the Hyatt Gold Passport program including the use of Free Night Awards and Suite Upgrade Awards, see goldpassport.com. This one-time bonus offer is valid only for first-time Hyatt Card cardmembers with new accounts. Previous and existing Hyatt Card cardmembers/accounts are not eligible for this bonus offer. Chase is not responsible for offer fulfillment. If your account is not open for at least 3 months, Hyatt and Chase reserve the right to deduct the Free Night Awards and Suite Upgrade Awards from your Hyatt Gold Passport account. Annual fee applies. For pricing details, please see Pricing & Terms.

DIAMOND MEMBERS:
To be eligible for this bonus offer, you must be an existing Hyatt Gold Passport Diamond member at the time of application. You will qualify for and receive your two Hyatt Gold Passport® Suite Upgrade Free Night Awards after your first purchase. First purchase does not include using your account for balance transfers or cash advances, or using any checks that access your account. Each Suite Upgrade Free Night Award is valid for one (1) night at participating Hyatt Hotels and Resorts for use within one year from date of issuance. Suites are not available at all Hyatt locations. Award may not be used with all suite types. Awards are not transferable. After qualifying, please allow 10 days for your Suite Upgrade Free Night Awards to post to your Hyatt Gold Passport account. For complete terms and conditions of the Hyatt Gold Passport program including the use of Suite Upgrade Free Night Awards, see goldpassport.com. This one-time bonus offer is valid only for first-time Hyatt Card cardmembers with new accounts. Previous and existing Hyatt Card cardmembers/accounts are not eligible for this bonus offer. Chase is not responsible for offer fulfillment. If your account is not open for at least 3 months, Hyatt and Chase reserve the right to deduct the Suite Upgrade Free Night Awards from your Hyatt Gold Passport account. Annual fee applies. For pricing details, please see Pricing & Terms.