In the past I've analyzed this and looked for hotels with top Tripadvisor ratings (4.5+). Based on this my comprehensive list of best places to use the free night at are:
- Andaz Savannah
- Hyatt Place Chicago/River North
- Hyatt at Olive 8
- Grand Hyatt Seattle
- Hyatt Escala Lodge at Park City
- Hyatt Place Austin Downtown
- Hyatt Market Street, The Woodlands
- Park Hyatt Toronto
- Andaz Peninsula Papagayo Resort
- Grand Hyatt at Baha Mar
- Hyatt Regency Trinidad
- Hyatt Regency Mexico City
- Grand Hyatt Melbourne
- Grand Hyatt Shenyang
- Andaz Xintiandi, Shanghai
- Grand Hyatt Beijing
- Grand Hyatt Macau
- Grand Hyatt Shanghai
- Hyatt Regency Hangzhou
- Hyatt Regency Hong Kong, Tsim Sha Tsui
- Hyatt on the Bund
- Grand Hyatt Mumbai
- Park Hyatt Goa Resort and Spa
- Park Hyatt Siem Reap
- Grand Hyatt Kuala Lumpur
- Park Hyatt Busan
- Park Hyatt Seoul
- Grand Hyatt Erawan Bangkok
- Hyatt Regency Hua Hin
- Park Hyatt Saigon
- Hyatt Capital Gate, Abu Dhabi
- Grand Hyatt Dubai
- Grand Hyatt Istanbul
- Hyatt Regency Dar Es Salaam, The Kilimanjaro
- Hyatt Regency Baku
- Park Hyatt Hamburg
- Hyatt Regency Cologne
- Grand Hyatt Berlin
- Grand Hyatt Sao Paulo (CAT 3)