In the City West district of Sydney is Broadway, Ultimo and Pyrmont, but not Glebe or Newtown which is in the Inner West. It lies between the City South, Darling Harbour and the Inner West. It contains Star City, and Pyrmont Bay, including Harris St.
The light-rail system that skirts the western side of Darling Harbour, and then runs past the Casino and the Fish Markets. It is an easy way of accessing the area if you are coming through Central Station, where the line commences. It runs 24/7 between Central Station and Casino stations, other stations have services every 10 minutes between 6AM and 11PM (midnight on Fri/Sat).
If coming from the City Centre, the 443 bus is your friend. The bus travels from George St in the City Centre, doing a loop around the entire Pyrmont and Ultimo area, before returning to the City Centre. Get back on where you got off. The bus runs every 10-15 minutes from around 6am until midnight.
If you are enthusiastic, the whole area can be walked from most points in the City Centre in 30 minutes or so, and less from Darling Harbour.
The City West pubs are tend to be quieter and less pretentious than those to the east of the city. There nearly a pub on every block, where you can get a seat and have a meal, and maybe watch a sporting match on the big screen, or have a game of pool. The crowd tends to be a blend of locals, longer stay backpackers, and a few Sydneysiders from outside the area.
However, the area surrounding the Casino and the street linking the Casino to Darling Harbour has a more active vibe.
Darling Harbour is just next door, with a selection of upmarket accommodation.
All the pubs have accommodation, varying in quality, offering a real alternative style from the normal city accommodation.
Star City has the obligatory large hotel rising above the Casino. Don't expect the kind of accommodation deals you would find in Las Vegas however, unless you quality for admission to the Inner Sanctum.
The rest of the city is just at your eastern doorstep, but if you have made it this far west, why not keep going to Sydney's nner West. Still plenty of restaurants and cafes, with a more inner-city residential feel. Simply hop on to the light rail to head on.