Sydney is a big city, well huge actually and there is a good diversity of aikido lineages and practices. Be sure to check out the Aikido Styles page. Choosing a dojo is a combination of something you can get to regularly, finding a quality teacher and doing a style that is compatable with your needs, fitness and intrests.
Aikido was first brought to Sydney in a big way by Seiichi Sugano sensei who formed Aikikai Australia, though it wasn't until it expanded and now headquartered in Melbourne that it really started to take off. There are a few dojo formed that may or may not be still affiliated and some that are independant like the Shin Sen which is reasonably well know (www.shinsendojo.com.au)
Today Sydney boasts many aikido dojo from many schools. In ~2008 Mic Marelli Sensei of Aiki Kunren began a collegiate approach for the city as a good way for them to interact, though i am not sure if it is still running. probably the largest lineage in Sydney is the Iwama Ryu, Ryu Ha because of the work of Saburo Takayasu (http://www.aikidoaus.com.au) with 7 dojo affiliated to him and others strongly influenced by him at one time or other.
Aikido Kenkyukai have strong presence in Sydney as recently establish a dedicated dojo there (http://www.aikidosydneycity.com/)
Andrew Sunter established 2 ki society dojos in the 90's and in 2002 followed Maruyama Sensei to Aikido Yuishinkai (www.aikidoinsydney.com). More recently Tony nel of several brisbane dojo relocated to Sydney and formed a dojo in Liverpool www.aikidoliverpool.com
More recent additions include Darren Friends Yoshinkan dojo ( www.aikido-sydney.com.au/ )and the Tomiki schools have a resurgance as well ( www.sydneyaikido.com.au/ )
The aikido centre http://aikidonsw.org.au/ was also kind enough to follow some of the work of this site (aikiphysics) so hope to visit them sometime too.