Here are some centres nearby with contact details.
Caring 4 Kids- Broadway shopping centre
http://caring4kids.com.au/broadway/
KU Ultimo Children's Centre
http://www.ku.com.au/ku.ultimo
Little Zak`s academy
http://www.littlezaks.com.au/centres/ultimo/
SDN Ultimo
http://www.sdn.org.au/services/our-centres/sdn-ultimo/
Kindy Patch
https://www.kindypatch.com.au/centres/ultimo-childcare/
Active kids World Tower
http://www.activekidsgroup.com.au/location/active-kids-world-tower/
George street Early learning centre
https://www.guardian.edu.au/childcare-early-learning-centres/nsw/sydney/george-street/
Explore& Develop
http://exploreanddevelop.com.au/explore-develop-castlereagh-street/