Newtown is a good possie SD.
For busses, the key is head to 'Newtown Bridge' - where the railway station is. Although busses go up and down King Street all day. They go down the highway between Newtown and Tempe and there are busses from there to Carlton/Kogarah. The Taj and Jubilee are on the Princes Hwy and King Street, Newtown is a part of the Princes Highway - but 7+ Kms north (I've walked from Newtown to Kogarah but its bit of a hike, takes an hour or more).
The trains are very handy. Basically: Newtown will take you west to Telstra. Erskineville will take you south to Kogarah.
Newtown train station is a fairly major station and will take you out to Homebush where Telstra is (probably about 12 or so stops). Erskineville Station is also very close to Newtown and all part of the mix - not as big as Newtwon but still has plenty of regular trains. Avoid nearby Macdonaldtown station unless you're into train spotting and like watching them whiz past.
Erskineville rail is on the southern line and will take you to Carlton Station (about 6-8 stops). St George Leagues is a short walk from there, about 5-10 mins. You'll walk straight down Jubilee Avenue and past the great ground itself.
As with any public transport, watch your timetables - check out the websites for cityrail at
http://www.cityrail.info - there's night bus link there as well but be wary of their relability late at night.
As always, you'll get there faster in a car or taxi. Newtown is pretty much on the same side of town but more inner-city. My guesstimate is that its a $15-20 taxi fare between Kogarah and Newtown.
You can't go wrong if you decide to meet up at the Taj. It'll be open till late.