This Hyatt is kinda old and not very close to the airport... I'm not sure if they have shuttles but I'd say skip it unless you wanna earn a stay/night credit.

Mall of Asia (MOA) is close, as well as Nayong Pilipino.... Better yet, you can spend the day at Bonifacio Global City (BGC) in Taguig which is more modern and lot more Westernized than MOA and not as far as Shangri-La in Makati or Hyatt. At least 40 mins (without traffic) from Terminal 1.

Just read up on the 2 kinds of cabs you get though (the pricier airport taxis and the haggling white taxis).